Question

# An article in the San Jose Mercury News stated that students in the California state university...

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 43 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?
Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

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

2. What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)

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

4. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) α =

5. 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.)

(i) =

(ii) =

(iii) =  The solution to this problem is given by