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;60;60;65;60;60;60;55;55.

• State the distribution to use for the test. (Enter your answer in the formzort_dfwheredfis the degrees of freedom.)
• What is the test statistic? (If using thezdistribution round your answers to two decimal places, and if using thetdistribution round your answers to three decimal places.)
• What is thep-value? (Round your answer to four decimal places.)
• 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.)

The mean age of De Anza College students in a previous term was 26.6 years old. An instructor thinks the mean age for online students is older than 26.6. She randomly surveys63online students and finds that the sample mean is29.8with a standard deviation of 2.1. Conduct a hypothesis test at the 5% level.

• State the distribution to use for the test. (Enter your answer in the formzort_dfwheredfis the degrees of freedom.)
• What is the test statistic? (If using thezdistribution round your answers to two decimal places, and if using thetdistribution round your answers to three decimal places.
• What is thep-value? (Round your answer to four decimal places.)
• Alpha (Enter an exact number as an integer, fraction, or decimal.)
• 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 answers to two decimal places.)