Answer:
sdvsdsdfdff
Step-by-step explanation:
log 3=.4771 log 5=.6990 find the value of log 150
Answer:
2.17609
Step-by-step explanation:
Easiest and fastest way is to just directly plug log base 10 of 150 into the calc, as it is a nasty decimal.
Which is the graph |3x-6|=21
Answer:
it should look like this
A courier service claims that 5% of all of its deliveries arrive late. Assuming the claim is true and deliveries are independent, a sample of 10 deliveries is randomly selected. What is the probability that more than 2 of the sample deliveries arrive late
Answer:
The probability that more than 2 of the sample deliveries arrive late = 0.0115
Step-by-step explanation:
This is a binomial distribution problem
A binomial experiment is one in which the probability of success doesn't change with every run or number of trials.
It usually consists of a fixed number of runs/trials with only two possible outcomes, a success or a failure. The outcome of each trial/run of a binomial experiment is independent of one another.
The probability of each delivery arriving late = 5% = 0.05
- Each delivery is independent from the other.
- There is a fixed number of deliveries to investigate.
- Each delivery has only two possible outcomes, a success or a failure of arriving late.
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = number of deliveries we're considering = 10
x = Number of successes required = number of deliveries that we expect to arrive late = more than 2 = > 2
p = probability of success = probability of a delivery arriving late = 0.05
q = probability of failure = probability of a delivery NOT arriving late = 0.95
P(X > 2) = 1 - P(X ≤ 2)
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
= 0.59873693924 + 0.31512470486 + 0.07463479852
= 0.98849644262
P(X > 2) = 1 - P(X ≤ 2)
= 1 - 0.98849644262
= 0.01150355738
= 0.0115
Hope this Helps!!!
The scores on the Wechsler Adult Intelligence Scale are approximately Normal with \muμ = 100 and \sigmaσ = 15. If you scored 130, your score would be higher than approximately what percent of adults?
Answer:
Your score would be higher than 97.72% of adults, that is, higher than approximately 98% of adults.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 100, \sigma = 15[/tex]
If you scored 130, your score would be higher than approximately what percent of adults?
To find the proportion of scores that are lower than, we find the pvalue of Z when X = 130. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{130 - 100}{15}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
0.9772*100 = 97.72%.
Your score would be higher than 97.72% of adults, that is, higher than approximately 98% of adults.
24 1/2 is equal to what decimal
Answer:
24.5
Step-by-step explanation:
24 = 24
1/2 -->
convert to a decimal => 1 divided by 2
0.5
24+0.5 = 24.5
Hope this helps!
A jar of marbles contains the following: two purple marbles, four white marbles, three blue marbles, and two green marbles. What is the probability of selecting a white marble from a jar of marbles?
Answer:
4/11
Step-by-step explanation:
Total number of marbles = 2(purple) + 4(white) + 3(blue) + 2(green)
= 11
Number of white marbles = 4
Probability of selecting a white marble =
number of white marbles/total number of marbles in the jar
= 4/11
The probability of selecting a white marble from a jar of marbles is 4/11.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Purple Marbles = 2
White Marbles = 4
Blue Marbles = 3
Green Marbles = 2
Total marbles= 2+ 4+ 3+ 2= 11
So, the probability of selecting a white marble from a jar of marbles
= 4/11
Hence, the probability is 4/11.
Learn more about probability here:
https://brainly.com/question/11234923
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A 2011 survey, by the Bureau of Labor Statistics, reported that 91% of Americans have paid leave. In January 2012, a random survey of 1000 workers showed that 89% had paid leave. The resulting p-value is .0271; thus, the null hypothesis is rejected. It is concluded that there has been a decrease in the proportion of people, who have paid leave from 2011 to January 2012. What type of error is possible in this situation?
Answer:
Is possible to make a Type I error, where we reject a true null hypothesis.
Step-by-step explanation:
We have a hypothesis test of a proportion. The claim is that the proportion of paid leave has significantly decrease from 2011 to january 2012. The P-value for this test is 0.0271 and the nunll hypothesis is rejected.
As the conclusion is to reject the null hypothesis, the only error that we may have comitted is rejecting a true null hypothesis.
The null hypothesis would have stated that there is no significant decrease in the proportion of paid leave.
This is a Type I error, where we reject a true null hypothesis.
Joe wants to saw a wooden plank into 3/4 -meter pieces. The length of the wooden plank is 15/4meters. How many 3/4 -meter pieces can Joe saw from the wooden plank?
Answer:
3 wooden plank he can saw
Answer:
he can saw 3 wooden planks
Step-by-step explanation:
Please help mehhh please!!
Answer:
1
Step-by-step explanation:
The mean is the average of the sum of all integers in a data set.
Caroline has 2 pieces of cheese, Samuel has 4 pieces of cheese, Abby has 4 pieces of cheese, and Jason has 2 pieces of cheese
2 + 4 + 4 + 2 = 12
12 divides by 4, since there are 4 people, to equal the mean
12 / 4 = 3
Now since we have the mean, find the distance from the mean to each number
3 - 2 = 1
4 - 3 = 1
4 - 3 = 1
3 - 2 = 1
1 + 1 + 1 + 1 = 4
4 / 4 = 1
The percentage of households that include at least one frequent gamer is 58%. A gaming magazine is interested in studying this further to see how it impacts their magazine advertisements. For what sample size, n, will the sampling distribution of sample proportions have a standard deviation of 0.02
Answer:
For a sample size of n = 609.
Step-by-step explanation:
Central limit theorem for proportions:
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
We have that p = 0.58.
We have to find n for which s = 0.02. So
[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
[tex]0.02 = \sqrt{\frac{0.58*0.42}{n}}[/tex]
[tex]0.02\sqrt{n} = \sqrt{0.58*0.42}[/tex]
[tex]\sqrt{n} = \frac{\sqrt{0.58*0.42}}{0.02}[/tex]
[tex](\sqrt{n})^{2} = (\frac{\sqrt{0.58*0.42}}{0.02})^{2}[/tex]
[tex]n = 609[/tex]
For a sample size of n = 609.
The height of the triangle is 10 cm. It is decreased by 25%. Calculate the new height.
Decreased height = 10 x [tex]\frac{100 - 25}{100}[/tex]
= 10 x [tex]\frac{75}{100}[/tex]
= [tex]\frac{750}{100}[/tex]
= 7.5 cm
Answer:
7.5 cm
Step-by-step explanation:
Decreased height = 25% of 10
[tex]=\frac{25}{100}*10\\\\=0.25*10\\=2.5[/tex]
New height = 10 - 2.5 = 7.5 cm
Which of the following is the solution to 9|x-1|=-45
Answer:
No solutions.
Step-by-step explanation:
9|x-1|=-45
Divide 9 into both sides.
|x-1| = -45/9
|x-1| = -5
Absolute value cannot be less than 0.
Answer:
No solution
Step-by-step explanation:
=> 9|x-1| = -45
Dividing both sides by 9
=> |x-1| = -5
Since, this is less than zero, hence the equation has no solutions
Please help me with this math problem
Answer:
-1/4 is the slope and the y intercept is -4
Step-by-step explanation:
Solve for y
x +4y = -16
Subtract x
4y = -x-16
Divide by 4
4y/4 = -x/4 -16/4
y = -1/4 x -4
This is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
-1/4 is the slope and the y intercept is -4
I need help please ASAPPP!
Answer:
16
Step-by-step explanation:
Please see attached photo for diagrammatic explanation.
Note: r is the radius
Using pythagoras theory, we can obtain the value of 'x' in the attached photo as shown:
|EB|= x
|FB| = 10
|EF| = 6
|EB|² = |FB|² – |EF|²
x² = 10² – 6²
x² = 100 – 36
x² = 64
Take the square root of both side.
x = √64
x = 8
Now, we can obtain line AB as follow:
|AB|= x + x
|AB|= 8 + 8
|AB|= 16
Therefore, line AB is 16
Luke and skylar work at furniture store. Luke is paid $180 per week plus 5% of his total sales in dollars ,x,which can be represented by g(x)=180+0.05x. Skylar is paid $104 per week plus 7% of her total sales in dollars which can be represented by f(x)=104+0.07x. Determine the value of x in dollars that will make their weekly pay the same
Answer:
The total sales in dollars to make their pay equal is: $ 3800
Step-by-step explanation:
Since we need to find the number of sales that make both function equal in value, we equal both expressions, and solve for 'x":
[tex]180+0.05 \,x=104+0.07 \,x\\180-104=0.07\,x-0.05\,x\\76=0.02x\\x=\frac{76}{0.02} \\x=3800[/tex]
Terry has a number cube that is numbered from 1 to 6. She rolls the cube 50 times. Which equation can be used to predict the number of times that she will roll a number that is greater than 4? P (number greater than 4) = StartFraction 1 over 6 EndFraction (50) P (number greater than 4) = StartFraction 2 over 6 EndFraction (50) P (number greater than 4) = StartFraction 3 over 6 EndFraction (50) P (number greater than 4) = StartFraction 4 over 6 EndFraction (50)
Answer:
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Does the graph represent a function. Explain
Answer:
Yes
Step-by-step explanation:
functions include parabolas so yes!
Expand 2x(5x-2)
Help please ?
Answer: 10x^2 - 4x
Step-by-step explanation:
To expand, you are not simplifying, so multiplying out is the answer here. To do this, use the distributive property. The distributive property in this case means that if you are multiplying one number by a whole expression inside parenthesis, multiply the one number by each term in the expression:
2x(5x - 2)
= 2x(5x) + 2x(-2)
= 10x^2 - 4x
The product of the expression is equivalent to -
10x² - 4x.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as follows -
2x(5x - 2)
The given expression is -
2x(5x - 2)
10x² - 4x
Therefore, the product of the expression is equivalent to -
10x² - 4x.
To solve more questions on expression evaluation, visit the link below -
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Can someone please help me??
Answer : The value of x is 4.1 cm.
Step-by-step explanation :
As we know that the perpendicular dropped from the center divides the chord into two equal parts.
That means,
AB = CB = [tex]\frac{15.6cm}{2}=7.8cm[/tex]
Now we have o calculate the value of x by using Pythagoras theorem.
Using Pythagoras theorem in ΔOBA :
[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]
[tex](OA)^2=(OB)^2+(BA)^2[/tex]
Now put all the values in the above expression, we get the value of side OB.
[tex](8.8)^2=(x)^2+(7.8)^2[/tex]
[tex]x=\sqrt{(8.8)^2-(7.8)^2}[/tex]
[tex]x=\sqrt{77.44-60.84}[/tex]
[tex]x=\sqrt{16.6}[/tex]
[tex]x=4.074\approx 4.1[/tex]
Therefore, the value of x is 4.1 cm.
A box contains 11 red chips and 4 blue chips. We perform the following two-step experiment: (1) First, a chip is selected at random from the box and is then removed from the box. (After this first step, there are 14 chips left in the box. ) (2) Then, a chip is selected at random from the box (that is, from the remaining 14 chips) . Let B 1 be the event that the chip removed from the box at the first step of the experi- ment is red. Let B 2 be the event that the chip removed from the box at the first step of the experiment is blue. Let A be the event that the chip selected from the box at the second step of the experiment is red.Find P(B1), P(B2), P(A), P(B1|A), and P(B2|A).
Answer:
P(B1) = (11/15)
P(B2) = (4/15)
P(A) = (11/15)
P(B1|A) = (5/7)
P(B2|A) = (2/7)
Step-by-step explanation:
There are 11 red chips and 4 blue chips in a box. Two chips are selected one after the other at random and without replacement from the box.
B1 is the event that the chip removed from the box at the first step of the experiment is red.
B2 is the event that the chip removed from the box at the first step of the experiment is blue. A is the event that the chip selected from the box at the second step of the experiment is red.
Note that the probability of an event is the number of elements in that event divided by the Total number of elements in the sample space.
P(E) = n(E) ÷ n(S)
P(B1) = probability that the first chip selected is a red chip = (11/15)
P(B2) = probability that the first chip selected is a blue chip = (4/15)
P(A) = probability that the second chip selected is a red chip
P(A) = P(B1 n A) + P(B2 n A) (Since events B1 and B2 are mutually exclusive)
P(B1 n A) = (11/15) × (10/14) = (11/21)
P(B2 n A) = (4/15) × (11/14) = (22/105)
P(A) = (11/21) + (22/105) = (77/105) = (11/15)
P(B1|A) = probability that the first chip selected is a red chip given that the second chip selected is a red chip
The conditional probability, P(X|Y) is given mathematically as
P(X|Y) = P(X n Y) ÷ P(Y)
So, P(B1|A) = P(B1 n A) ÷ P(A)
P(B1 n A) = (11/15) × (10/14) = (11/21)
P(A) = (11/15)
P(B1|A) = (11/21) ÷ (11/15) = (15/21) = (5/7)
P(B2|A) = probability that the first chip selected is a blue chip given that the second chip selected is a red chip
P(B2|A) = P(B2 n A) ÷ P(A)
P(B2 n A) = (4/15) × (11/14) = (22/105)
P(A) = (11/15)
P(B2|A) = (22/105) ÷ (11/15) = (2/7)
Hope this Helps!!!
Solve 2cos3x=0.9.
Pls help me with this trigonometric equations with multiple angles.
Answer:
[tex]x=\frac{cos^{-1}(0.45)+2n\pi}{3} ,x=\frac{2\pi- cos^{-1}(0.45)+2n\pi}{3}[/tex]
Step-by-step explanation:
Given: [tex]2 cos(3x)=0.9[/tex]
To find: solutions of the given equation
Solution:
Triangle is a polygon that has three sides, three angles and three vertices.
Trigonometry explains relationship between the sides and the angles of the triangle.
Use the fact: [tex]cos x=a[/tex]⇒[tex]x=cos^{-1}(a)+2n\pi,x=2\pi-cos^{-1}(a)+2n\pi[/tex]
[tex]2 cos(3x)=0.9[/tex]
Divide both sides by 2
[tex]cos(3x)=\frac{0.9}{2}=0.45[/tex]
[tex]3x=cos^{-1}(0.45)+2n\pi,3x=2\pi- cos^{-1}(0.45)+2n\pi[/tex]
So,
[tex]x=\frac{cos^{-1}(0.45)+2n\pi}{3} ,x=\frac{2\pi- cos^{-1}(0.45)+2n\pi}{3}[/tex]
A newsletter publisher believes that less than 29% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.02 level to substantiate the publisher's claim? State the null and alternative hypotheses for the above scenario.
Answer:
For this case they want to proof if the proportion of readers own a Rolls royce is less than 0.29 and that wuld be the alternative hypothesis. The complement would represent the null hypothesis. Then the system of hypothesis for this case are:
Null hypothesis: [tex] p \geq 0.29[/tex]
Alternative hypothesis: [tex]p< 0.29[/tex]
Step-by-step explanation:
For this case they want to proof if the proportion of readers own a Rolls royce is less than 0.29 and that wuld be the alternative hypothesis. The complement would represent the null hypothesis. Then the system of hypothesis for this case are:
Null hypothesis: [tex] p \geq 0.29[/tex]
Alternative hypothesis: [tex]p< 0.29[/tex]
Frederick took out a 20-year loan for $70,000 at an APR of 2.2%, compounded monthly. Approximately how much would he save if he paid it off 9 years early?
Answer:
$38,645.7208
Step-by-step explanation:
Given that
Principal = $70,000
Time = 20 years
Rate = 2.2%
The calculation of the amount of saving is shown below:-
[tex]=P(1+r)^t[/tex]
A = Future amount
P = Principal amount
[tex]r = \frac{APR}{12}[/tex]
[tex]r = \frac{0.022}{12}[/tex]
0.001833333
t = 20 years which is equals to 240 months
[tex]A=\$70,000\times (1+0.001833333)^{240}[/tex]
[tex]A=\$70,000\times 1.552081726[/tex]
= $108,645.7208
And, the loan amount for 20 years is $70,000
So,
He would save by paying off 9 years early is
= $108,645.7208 - $70,000
= $38,645.7208
Its $3644.67 since everyone couldn't find it solved it myself ;)
Pleassseee hhheeelllppp
Answer/Step-by-step explanation:
When solving problems like this, remember the following:
1. + × + = +
2. + × - = -
3. - × + = -
4. - × - = +
Let's solve:
a. (-4) + (+10) + (+4) + (-2)
Open the bracket
- 4 + 10 + 4 - 2
= - 4 - 2 + 10 + 4
= - 6 + 14 = 8
b. (+5) + (-8) + (+3) + (-7)
= + 5 - 8 + 3 - 7
= 5 + 3 - 8 - 7
= 8 - 15
= - 7
c. (-19) + (+14) + (+21) + (-23)
= - 19 + 14 + 21 - 23
= - 19 - 23 + 14 + 21
= - 42 + 35
= - 7
d. (+5) - (-10) - (+4)
= + 5 + 10 - 4
= 15 - 4 = 11
e. (-3) - (-3) - (-3)
= - 3 + 3 + 3
= - 3 + 9
= 6
f. (+26) - (-32) - (+15) - (-8)
= 26 + 32 - 15 + 8
= 26 + 32 + 8 - 15
= 66 - 15
= 51
Find two consecutive even integers whose sum is -50. Which of the following equations could be used to solve the problem? A) 2 x + 2 = -50 B) 2 x = -50 C) 2 x + 1 = -50 D) x^2 + 1= -50
Answer:
[tex]2x+2=-50[/tex]
Step-by-step explanation:
[tex]x+2=y\\x+y=-50\\x+x+2=-50\\2x+2=-50[/tex]
The equation that can be used to find out [tex]x[/tex] and [tex]y[/tex] is [tex]2x+2=-50[/tex]
Answer:
[tex]\mathrm{A}[/tex]
Step-by-step explanation:
Two consecutive even integers.
The first integer is even and can be as [tex]x[/tex]
The second integer is also even and can be as [tex]x+2[/tex]
Their sum is [tex]-50[/tex]
[tex]x+x+2=-50[/tex]
[tex]2x+2=-50[/tex]
Please answer this correctly
Description:
As we that that 3 of the students voted for counting .
4 Students voted for sorting
6 Students voted for shapes
7 Students voted for addition
Answer:
Counting - 3%
Sorting - 4%
Shapes- 6%
Addition- 7%
Please mark brainliest
Hope this helps.
Answer:
Counting: 15%
Sorting: 20%
Shapes: 30%
Addition: 35%
Step-by-step explanation:
Counting: [tex]\frac{3}{3+4+6+7} =\frac{3}{20} =\frac{15}{100} =[/tex] 15%
Sorting: [tex]\frac{4}{3+4+6+7} =\frac{4}{20} =\frac{20}{100} =[/tex] 20%
Shapes: [tex]\frac{6}{3+4+6+7} =\frac{6}{20} =\frac{30}{100} =[/tex] 30%
Addition: [tex]\frac{7}{3+4+6+7} =\frac{7}{20} =\frac{35}{100} =[/tex]35%
A lumber company is making doors that are 2058.0 millimeters tall. If the doors are too long they must be trimmed, and if the doors are too short they cannot be used. A sample of 22 is made, and it is found that they have a mean of 2045.0 millimeters with a standard deviation of 13.0. A level of significance of 0.1 will be used to determine if the doors are either too long or too short. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.
Answer:
[tex]t=\frac{2045-2058}{\frac{13}{\sqrt{22}}}=-4.69[/tex]
The degrees of freedom are given by:
[tex]df=n-1=22-1=21[/tex]
And the p value would be given by:
[tex]p_v =2*P(t_{21}<-4.69)=0.000125[/tex]
Since the p value is a very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2058 mm at the significance level of 0.1 (10%) given
Step-by-step explanation:
Information given
[tex]\bar X=2045[/tex] represent the sample mean
[tex]s=13[/tex] represent the standard deviation
[tex]n=22[/tex] sample size
[tex]\mu_o =2058[/tex] represent the value to test
[tex]\alpha=0.1[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to cehck if the true mean for this case is equal to 2058 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 2058[/tex]
Alternative hypothesis:[tex]\mu \neq 2058[/tex]
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]t=\frac{2045-2058}{\frac{13}{\sqrt{22}}}=-4.69[/tex]
The degrees of freedom are given by:
[tex]df=n-1=22-1=21[/tex]
And the p value would be given by:
[tex]p_v =2*P(t_{21}<-4.69)=0.000125[/tex]
Since the p value is a very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2058 mm at the significance level of 0.1 (10%) given
The waiting time in line at an ice cream shop has a uniform distribution between 3 and 14 minutes. What is the 75th percentile of this distribution? (Recall: The 75th percentile divides the distribution into 2 parts so that 75% of area is to the left of 75th percentile) _______ minutes Answer: (Round answer to two decimal places.)
Answer:
The 75th percentile of this distribution is 11 .25 minutes.
Step-by-step explanation:
The random variable X is defined as the waiting time in line at an ice cream shop.
The random variable X follows a Uniform distribution with parameters a = 3 minutes and b = 14 minutes.
The probability density function of X is:
[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b;\ a<b[/tex]
The pth percentile is a data value such that at least p% of the data-set is less than or equal to this data value and at least (100-p)% of the data-set are more than or equal to this data value.
Then the 75th percentile of this distribution is:
[tex]P (X < x) = 0.75[/tex]
[tex]\int\limits^{x}_{3} {\frac{1}{14-3}} \, dx=0.75\\\\ \frac{1}{11}\ \cdot\ \int\limits^{x}_{3} {1} \, dx=0.75\\\\\frac{x-3}{11}=0.75\\\\x-3=8.25\\\\x=11.25[/tex]
Thus, the 75th percentile of this distribution is 11 .25 minutes.
The sum of a number and twice the number is 24 what is the number?
Answer:
x = 8
Step-by-step explanation:
Step 1: Write out the expression
x + 2x = 24
Step 2: Combine like terms
3x = 24
Step 3: Isolate x
x = 8
And we have our final answer!
Answer:
X=8
Step-by-step explanation:
A publisher reports that 65% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 340 found that 60% of the readers owned a laptop. State the null and alternative hypotheses. Answer
Answer:
[tex]z=\frac{0.60 -0.65}{\sqrt{\frac{0.65(1-0.65)}{340}}}=-1.933[/tex]
The p value for this case can be calculated with this probability:
[tex]p_v =2*P(z<-1.933)=0.0532[/tex]
For this case is we use a significance level of 5% we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is different from 0.65 or 65%. We need to be careful since if we use a value higher than 65 for the significance the result would change
Step-by-step explanation:
Information given
n=340 represent the random sample taken
[tex]\hat p=0.60[/tex] estimated proportion of readers owned a laptop
[tex]p_o=0.65[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v{/tex} represent the p value
Hypothesis to test
We want to check if the true proportion of readers owned a laptop if different from 0.65
Null hypothesis:[tex]p=0.65[/tex]
Alternative hypothesis:[tex]p \neq 0.65[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing we got:
[tex]z=\frac{0.60 -0.65}{\sqrt{\frac{0.65(1-0.65)}{340}}}=-1.933[/tex]
The p value for this case can be calculated with this probability:
[tex]p_v =2*P(z<-1.933)=0.0532[/tex]
For this case is we use a significance level of 5% we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is different from 0.65 or 65%. We need to be careful since if we use a value higher than 65 for the significance the result would change