A genetic experiment with peas resulted in one sample of offspring that consisted of 432 green peas and 164 yellow peas. a. Construct a 95% confidence interval to estimate of the percentage of yellow peas. b. It was expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations?

Answer:

The 95% confidence interval is $0.2392 < p < 0.3108$

No, the confidence interval includes 0.25, so the true percentage could easily equal 25%

Step-by-step explanation:

From the question we are told that

The total sample size is $n = 432 + 164 =596$

The number of offspring that is yellow peas is $y = 432$

The number of offspring that is green peas is $g = 164$

The sample proportion for offspring that are yellow peas is mathematically evaluated as

$\r p = \frac{ 164 }{596}$

$\r p = 0.275$

Given the the confidence level is 95% then the level of significance is mathematically represented as

$\alpha = (100 - 95)\%$

$\alpha = 5\% = 0.0 5$

The critical value of $\frac{\alpha }{2}$ from the normal distribution table is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically evaluated as

$E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1- \r p )}{n} }$

=> $E = 1.96 * \sqrt{\frac{0.275 (1- 0.275 )}{596} }$

=> $E = 0.0358$

The 95% confidence interval is mathematically represented as

$\r p - E < p < \r p + E$

=> $0.275 - 0.0358 < p < 0.275 + 0.0358$

=> $0.2392 < p < 0.3108$

6 0

3 years ago

A marketing researcher is investigating where consumers go to shop for produce. In a survey, consumers are asked to choose where

denpristay [2]

Answer: C.

Step-by-step explanation:

8 0

3 years ago

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Two professors at a nearby university want to co-author a new textbook in either economics or statistics. They feel that if they

WARRIOR [948]

Answer:

0.3 or 30%

Step-by-step explanation:

The professors will only seek a smaller publisher if they cannot place the statistics book with a major publisher. If the probability of getting a major publisher is 40% and the probability of getting a smaller publisher is 50%, then the probability that the statistics book would wind up being placed with a smaller publisher is given by:

$P=(1-P(major))*P(minor)\\P=(1-0.4)*0.5\\P=0.3$

The probability is 0.3 or 30%.

3 0

4 years ago