5. You survey 400 likely voters. 215 respond that they would vote for the incumbent and 185 respond that they would vote

[answerhappygod]

5 You Survey 400 Likely Voters 215 Respond That They Would Vote For The Incumbent And 185 Respond That They Would Vote 1 (273.82 KiB) Viewed 95 times

5. You survey 400 likely voters. 215 respond that they would vote for the incumbent and 185 respond that they would vote for the challenger. Let p be the fraction of all likely voters who prefer the incumbent and be the fraction of survey respondents who prefer the incumbent. (a) Use the survey responses to estimate p, i.e. calculate (b) Use the estimator for the variance of ô, ô(1 – Ô)/n to calculate the standard error of your estimator (c) What is the p-value for the test of Ho : p=0.5, vs H : p=0.5 (d) What is the p-value for the test of Ho : p = 0.5, vs H1 : p > 0.5 (e) In words, why do the results from c) and d) differ? (f) Construct the 95% confidence interval for p (g) Construct the 99% confidence interval for p (h) Based on your confidence intervals only, test the hypothesis that Ho : p = 0.5, vs Hư: P0.5 at the 5% significance level. 6. Data on fifth grade test scores for 420 school districts in California are given in the ‘CASchools' data accessed using the R code given in class. Denote as Y the simple average of reading and math test scores calculated in class. (a) Calculate the sample mean 7 (b) Calculate the sample standard deviation sy (c) Construct the 95% confidence interval for the mean test score in the population. (d) Divide the data into those with small classes (< 20 students per teacher) and large classes (> 20 students per teacher). Calculate 7 and sy for each group. Note the sample size for each. (e) Is there statistically significant evidence the districts with smaller class sizes have higher test scores? Explain your answer.