An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 38 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level?

1.State the null hypothesis.

2.State the alternative hypothesis.

3.In words, state what your random variable X represents.

X

represents the average number of students who receive an undergraduate degree in California.

X

represents the average number of students in the California university system.

X

represents the length of time it takes a student to finish his or her undergraduate degree.

X

represents the average length of time it takes students to finish their undergraduate degrees.

4.State the distribution to use for the test. (Enter your answer in the form z or t_df where df is the degrees of freedom.)

5. What is the test statistic?

6. What is the p-value? (Round your answer to four decimal places.)

7. Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value.

8. Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and an appropriate conclusion.(i) Alpha (Enter an exact number as an integer, fraction, or decimal.) = (ii) Decision:reject the null hypothesisdo not reject the null hypothesis (iii) Reason for decision:Since < p-value, we reject the null hypothesis.Since > p-value, we reject the null hypothesis. Since > p-value, we do not reject the null hypothesis.Since < p-value, we do not reject the null hypothesis. (iv) Conclusion:There is sufficient evidence to conclude that the average time it takes to finish the undergraduate degrees is longer than 4.5 years.There is not sufficient evidence to conclude that the average time it takes to finish the undergraduate degrees is longer than 4.5 years.

9.

Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper bounds to two decimal places.)