A random sample of 100 students is taken from a larger population of students in a multi-lecture course and the sample mean (average) of their final grades is found to be 62.25. Suppose that the population standard deviation is known to be 3. Which of the following is correct?

a.The true population mean grade is 62.25.

b.A 95% Z confidence interval for the true population mean that is calculated from this sample data of 100 students will be narrower than a 90% Z confidence interval for the true population mean that is calculated from this sample data of 100 students.

c.A 90% Z confidence interval for the true population mean that is calculated from this sample data of 100 students will be wider than a 95% Z confidence interval for the true population mean that is calculated from this sample data of 100 students.

d.A 90% Z confidence interval for the true population mean that is calculated from this sample data of 100 students would be narrower than a 90% Z confidence interval for the true population mean that is calculated from a sample of 81 students from the same population.

A random sample of 100 students is taken from a larger population of students in a multi-lecture course and the sample mean (average) of their final grades is found to be 57.5. Suppose it is known that the population standard deviation is 5. Use R to help you test, with a significance level of 0.01, whether there is significant evidence that the average grade for the population exceeds 56. Choose the most correct statement.

a.

You test Ho: <= 56 versus Ha: > 56 and you obtain a p-value of 0.001 (TO 3 DECIMALS) and the result is not significant.

b.

You test Ho: < 56 versus Ha: > 56 and you obtain a p-value of 0.001 (TO 3 DECIMALS) and the result is not significant.

c.

You test Ho: <= 56 versus Ha: > 56 and you obtain a pvalue of 0.001 (TO 3 DECIMALS) and the result is significant.

d.

You test Ho: > = 56 versus Ha: < 56 and you obtain a p-value of 0.001 (TO 3 DECIMALS) and the result is not significant.

A random sample of 100 students is taken from a larger population of students in a multi-lecture course and the sample mean (average) of their final grades is 58. Suppose it is known that the population standard deviation is 5. Use R to help you test, with a significance level of 0.01, whether there is significant evidence that the average grade for the population is below 59. Which of the following statements is most correct?

a.Your pvalue is 0.023 and you cannot reject your null hypothesis.

b.Your pvalue is 0.977 and you cannot reject your null hypothesis.

c.Your pvalue is 0.023 and you can reject your null hypothesis.

d.Your pvalue is 0.977 and you can reject your null hypothesis