1) a genetic experiment with peas resulted in one sample of offspring that consi

Question

1) a genetic experiment with peas resulted in one sample of offspring that consisted of 430 green peas and 163 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?

2) An online site presented this question, "Would the recent norovirus outbreak deter you from taking a cruise?" Among the 34,031 people who responded,67%

answered "yes." Use the sample data to construct a 90% confidence interval estimate for the proportion of the population of all people who would respond "yes" to that question. Does the confidence interval provide a good estimate of the population proportion?

3)

During a period of 11 years 1470 of the people selected for grand jury duty were sampled, and 33% of them were immigrants. Use the sample data to construct a 99% confidence interval estimate of the proportion of grand jury members who were immigrants. Given that among the people eligible for jury duty, 35.6 % of them were immigrants, does it appear that the jury selection process was somehow biased against immigrants?

4)

A study of 420,027 cell phone users found that 135 of them developed cancer of the brain or nervous system. Prior to this study of cell phone use, the rate of such cancer was found to be 0.0338 for those not using cell phones. Complete parts (a) and (b).

a. Use the sample data to construct a 95% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system.

5) Use the given data to find the minimum sample size required to estimate a population proportion or percentage. Margin of error: 0.01;confidence level 90%;

n=?

6)

Explanation / Answer

Q1.
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
No. of success(x)=163
Sample Size(n)=430
Sample proportion = x/n =0.379
Confidence Interval = [ 0.379 ±Z a/2 ( Sqrt ( 0.379*0.621) /430)]
= [ 0.379 - 1.96* Sqrt(0.001) , 0.379 + 1.96* Sqrt(0.001) ]
= [ 0.333,0.425]
Interpretations:
1) We are 95% sure that the interval [0.333 , 0.425 ] contains the true population proportion
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population proportion  
the percentage of offspring yellow peas is not 25%

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