A genetic experiment with peas resulted in one sample of offspring that consisted of 438 green peas and 173 yellow peas.

Required:
a. Construct a 95â% confidence interval to estimate of the percentage of yellow peas.
b. It was expected thatâ 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is notâ 25%, do the results contradictâ expectations?

Answers

Answer 1

Answer:

a

The 95% confidence interval is [tex] 0.2474 < p < 0.3188 [/tex]

b

  The result obtained does not contradict expectation

Step-by-step explanation:

From the question we are told that

   The number of green peas is  k =  438

   The number of yellow peas is u =  173

Generally the sample size is mathematically represented as

       [tex]n = k + u[/tex]

=>    [tex]n = 438 + 173[/tex]

=>    [tex]n = 611[/tex]

Generally the sample proportion for yellow peas is

      [tex]\^ p = \frac{u}{n}[/tex]

=>   [tex]\^ p = \frac{173}{611 }[/tex]

=>   [tex]\^ p = 0.2831[/tex]

From the question we are told the confidence level is  95% , hence the level of significance is    

      [tex]\alpha = (100 - 95 ) \%[/tex]

=>   [tex]\alpha = 0.05[/tex]

Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is  

   [tex]Z_{\frac{\alpha }{2} } =  1.96[/tex]

Generally the margin of error is mathematically represented as  

     [tex]E =  Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } [/tex]

=>  [tex]E =  1.96 * \sqrt{\frac{ 0.2831 (1- 0.2831)}{611} } [/tex]

=>  [tex]E =  0.0357 [/tex]

Generally 95% confidence interval is mathematically represented as  

      [tex]\^ p -E <  p <  \^ p +E[/tex]

=>     [tex] 0.2831  -0.0357 <p< 0.2831  + 0.0357[/tex]

=>     [tex] 0.2474 < p < 0.3188 [/tex]

From the question we are told that it was expected that 25% of the offspring peas will be yellow

   Now from the 95% confidence interval obtained we see that the expected sample proportion(25% ) falls within it so  it means that the result obtained does not contradict expectation


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