Question

For the situation below, construct the 95% confidence interval estimate to the population. assume that the results are based on a nationally representative sample. Express the estimate in a sentence. Of the 998 respondents questioned, 246 identified themselves as Catholic. Problem 2: The 40-hour work week is generally considered as a standard in American society today. Using data from the 2006 General Social Survey, you wish to determine whether the mean number of hours worked per week by men in the sample differs from the 40-hour standard. Use all or some of the information below to calculate the value of the single sample t-statistic. 65 Weekly Hours Worked Men Range Minimum value Maximum value Mean Variance Standard deviation 42.31 100.00 10.00 1,227 291 Sum Number of observations

Answer 1

1.)

P= x/n = 246/998 = 0.2465

critical value at 95% confidence interval(Z_a/2)=1.96

Confidence interval is given by:

PtZ2/2*1*(1-) 0.2465 * (1 – 0.2465) 0.2465 +1.96 * 998 = 0.2465 + 0.02674 = (0.21976, 0.27324)

2.)

Ho:u= 40 H1: +40 - = 1.24 - 3 - 42.31 - 40 test statistic(t) = 7 s/n 10/29 degree of freedom = n - 1 = 28 p- value = P(t < 11.241) = 2253

here we can see that p-value is very large (>>>0.05), fail to reject null hypothesis.

There is not enough evidence to support the claim that mean is different from 40