In an effort to make children’s toys safer and more tamperproof, toy packaging has become cumbersome for parents to remove in many cases. Accordingly, the director of marketing at Toys4Tots, a large toy manufacturer, wants to evaluate the effectiveness of a new packaging design that engineers claim will reduce customer complaints by more than 10 percentage points. Customer satisfaction surveys were sent to 220 parents who registered toys packaged under the old design and 220 parents who registered toys packaged under the new design. Of these, 86 parents expressed dissatisfaction with packaging of the old design, and 41 parents expressed dissatisfaction with packaging of the new design.
Let p1 represent the population proportion of parents that expressed dissatisfaction with the packaging of the old design and p2 represent the population proportion of parents that expressed dissatisfaction with the packaging of the new design.
A. Specify the null and alternative hypotheses to test for whether the proportion of customer complaints has decreased by more than 5% under the new packaging design.
1. H0 : p1 - p2 < 0.10; HA : p1 - p2 > 0.10
2. H0 : p1 - p2 = 0.10; HA : p1 - p2 is not equal to 0.10
3. H0 : p1 - p2 > 0.10; HA : p1 - p2 < 0.10
B. What is the value of the test statistic and the associated p-value?
C. At the 1% significance level, do the results support the engineers' claim?
D. At the 10% significance level, do the results support the engineers' claim?

Answer:

Explained below.

Step-by-step explanation:

(a)

In this case we need to determine if the proportion of customer complaints has decreased by more than 10% under the new packaging design.

The hypothesis can be defined as follows:  

H₀: The proportion of customer complaints has not decreased by more than 10% under the new packaging design, i.e. p₁ - p₂ ≤ 0.10.  

Hₐ: The proportion of customer complaints has decreased by more than 10% under the new packaging design, i.e. p₁ - p₂ > 0.10.  

(b)

The information provided is:

n₁ = 220

n₂ = 220

X₁ = 86

X₂ = 41

Compute the sample proportions and total proportions as follows:

[tex]\hat p_{1}=\frac{X_{1}}{n_{1}}=\frac{86}{220}=0.3909\\\\\hat p_{2}=\frac{X_{2}}{n_{2}}=\frac{41}{220}=0.1864\\\\\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{86+41}{220+220}=0.2886[/tex]

Compute the test statistic value as follows:

 [tex]z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)[\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}[/tex]

   [tex]=\frac{0.3909-0.1864}{\sqrt{0.2886(1-0.2886)\times[\frac{1}{220}+\frac{1}{220}]}}\\\\=\frac{0.2045}{\sqrt{0.0018665}}\\\\=4.733524\\\\\approx 4.73[/tex]

The test statistic value is 4.73.

Compute the p-value as follows:

[tex]p-value=P(Z>4.73)[/tex]

               [tex]=1-P(Z<4.73)\\=1-(\approx 1)\\=0[/tex]

The p-value of the test is 0.

(c)

The decision rule is:

The null hypothesis will be rejected if the p-value of the test is less than the significance level.

p-value = 0 < α = 0.01.

The null hypothesis will be rejected at 1%significance level.

Thus, there is enough evidence at 1% significance level to support the engineers' claim.

(d)

The decision rule is:

The null hypothesis will be rejected if the p-value of the test is less than the significance level.

p-value = 0 < α = 0.10.

The null hypothesis will be rejected at 10%significance level.

Thus, there is enough evidence at 10% significance level to support the engineers' claim.

Can someone solve this for me please?

Solve using the standard algorithm the area model the distributive property or the partial products method 2,809x4

Find the value of x in the figure given that SU = 70.

Solve 6y + 2x = 14 for x.

List the integers from least to greatest

{-6, -13, 0, 3, 5, - 7}

Use the image to answer the question below. 10 8 A B 10 8 10 -10 Which series of transformations would result in a figure that is congruent to the triangle ABC?​

how do i put this into factored form? (x-4)^2-9=0

3x - 6 + 4 = -20
Solve the multi-step equation and place the steps in the correct order.
ITEM BANK: Move to Bottom
3x - 2 = -20
3x - 6 + 4 = -20
3x = -18
x = -6
1
drag and drop answer here
2
drag and drop answer here
3
drag and drop answer here
4
drag and drop answer here

What is the slope of this graph?

A. -1/3

B. -3

C. 3

D. 1/3

What is the equation of this line? (shown in picture)

A. Y = -1/4x

B. Y = 4x

C. Y = -4x

D. Y = 1/4x

What is the greatest perfect square that is a factor of 392

A. 48+1.2m>40
B. 40+1.2m<48
C. 48+1.2m<40
D. 40+1.2m>48

will made his mini pecan tarts for the southern themed school party he bought 20 pounds (320 ounces) of pecans for $78.40 he put 2 ounces of pecans in each pecan tart he made what was the cost of the pecans in each mini pecan tart

What does 3g=
In math 8th grade

A box contains one each of $1, $5, $10, $20, and $100 bills. It costs $14 to reach in and withdraw one bill. What is the expected value?

Which expression is equal to 2rad-28 ​

Which of these numbers are perfect squares or perfect cubes? Select all that apply
A. 8
B. 16
C. 32
D. 64
E. 128

Do you think that students should be proficient in addition before learning multiplication?


answer in 175 words! thank you so much :)

The question to this is that it says jamie draws figure RSTU in the coordinate plane, as shown. Then he reflects Figure RSTU across the x-axis to form figure R’S’T’U’. I need the answer plzz help me

the perimeter of a rectangular pool is 258 m. If the width of the pool is 52 m, what is its length?

You never scale down to write a complex rate as a unit rate. True or false?

When 12 is divided by 2/3 which statement about the quotient is true?

Which statement is true about the graphs of the two lines y = x + 2 and y = x ?

Which of the following statements is true concerning ABC below?

What is the mean age of dogs at the dog park?

The expression −8x3(7x6 − 3x5) is equivalent to?

Do these ratios make a proportion? 4:10 and 6:15

I NEED THIS ASAP!!! Thanks!

how do you divide 78.74 divided by 12.7 in steps

y-2/3(9x - 3y)


With solution

What is a more economical purchase, a 5-pound box of spaghetti priced at $6.02, or a 1.5-pound box for $1.70?