Question

The mean work week for engineers in a start-up company is believed to be about 60 hours. A newly hired engineer hopes that it's shorter. She asks 10 engineering friends in start-ups for the lengths of their mean work weeks. Based on the results that follow, should she count on the mean work week to be shorter than 60 hours? Conduct a hypothesis test at the 5% level.

Data (length of average work week): 70; 50; 55; 65; 65; 55; 60; 55; 55; 60.

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 mean & null hypothesis

2. 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.)

3. 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.)

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

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.)

Answer 1