1.) In order to test a new production method, 15 employees were selected randomly to try the new method. The mean production rate for the sample was 80 parts per hour (with sample SD 10 parts per hour).

a. Calculate a standard error for the sample mean production rate for the new method.

b. The mean production rate under the old method is known to be 70 parts per hour. Is the new method rate significantly different, or is this just luck-of-the-draw on the employees sampled? Perform all the steps of the hypothesis test. Test at the 5% significance level.

2.) The proportion of homeowners with pets used to be 0.82. An animal adoption agency thinks in recent years this proportion has changed. In fact, out of 137 respondents, 102 reported having at least one pet. At the 5% level of significance, can you conclude that pet ownership has decreased recent years?

3.) Fifteen customers were asked to rate (on a scale of 1 to 10) their overall experience at a hotel before and after new management took over. The average difference for the sample (before - after) was found to be -2.45, with a difference in standard deviation of 1.23. Is there evidence at the 5% significance level that the average rating is higher after new management took over than before?