1 -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 4.5. Which of the following is correct? (Note that you can answer these questions from understanding gleaned in lecture and lab, but may find R helpful.)

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 99% Z confidence interval for the true population mean that is calculated from this sample data of 100 students.

A 95% Z confidence interval for the true population mean that is calculated from this sample of 100 students will be wider than a 99% Z confidence interval for the true population mean that is calculated from this sample data of 100 students.

The true population mean grade is 62.25.

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 144 students from the same population.

2-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 it is known that the population standard deviation is 3.2. You wish to determine whether the average grade for the population differs from 62. Use R to get the needed Z critical value and then createa 90% Z confidence interval for the average final grade for the population by hand. Choose the correct statement below.

The test is not significant at the 10% significance level because 62 is inside the confidence interval you created.

The test is significant at the 10% significance level because 62 is inside the confidence interval you created.

The test is not significant at the 10% significance level because 62.25 is inside the confidence interval you created.

The test is significant at the 10% significance level because 62 is outside the confidence interval you created.

3-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 56. Suppose it is known that the population standard deviation is 4. Use R to help you test, with a significance level of 0.02, whether there is significant evidence that the average grade for the population is below 57. Which of the following statements is most correct?

Your pvalue is 0.006 and you can reject your null hypothesis.

Your pvalue is 0.006 and you cannot reject your null hypothesis.

Your pvalue is 0.994 and you can reject your null hypothesis.

Your pvalue is 0.994 and you cannot reject your null hypothesis.

4 -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 8. Use R to help you test, with a significance level of 0.04, whether there is significant evidence that the average grade for the population exceeds 56. Choose the most correct statement.

You test Ho: <= 56 versus Ha: > 56 and you obtain a pvalue of 0.030 (TO 3 DECIMALS) and the result is significant.

You test Ho: > = 56 versus Ha: < 56 and you obtain a p-value of 0.030 (TO 3 DECIMALS) and the result is not significant.

You test Ho: <= 56 versus Ha: > 56 and you obtain a p-value of 0.030 (TO 3 DECIMALS) and the result is not significant.

You test Ho: < 56 versus Ha: > 56 and you obtain a p-value of 0.030 (TO 3 DECIMALS) and the result is not significant.

5_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 67. Suppose it is known that the population standard deviation is 4. You test whether there is significant evidence that the population average differs from 68, using a level of significance of 1%. Choose the most correct statement. Note: You will have to calculate the test statistic by hand, but you can use R to get your pvalue.

Your pvalue statement is 2P(Z > 2.50), your pvalue is 0.0248 and your decision is to fail to reject Ho

Your pvalue statement is 2P(Z > 2.50), your pvalue is 0.0062, and your decision is reject Ho.

Your pvalue statement is 2P(Z > 2.50), your pvalue is 0.0124 and your decision is to fail to reject Ho

Your pvalue statement is 2P(Z > 2.50 ), your pvalue is 0.0124 and your decision is to reject Ho.