Instructions: Turn in your homework in a word file and upload in Canvas under the designated Homework #4 assignment. Use complete sentences when answering the questions (half of the points can be deducted if you do not follow this instruction). Show your work and calculations for hand calculated questions, and show relevant SPSS tables for those questions not calculated by hand. Be sure to include only the relevant SPSS tables and output for each question. If you paste excess SPSS output, up to 50% points will be deducted.

1. (12pts) Below are the prices per gallon of gas from a random sample of gas stations in Columbia in 2012. A reporter hypothesizes that the mean gas rates in Columbia in 2012 rose above the mean price of $3.57 the previous year (2011).

3.48 3.51 3.52 3.53 3.54 3.55 3.56 3.57 3.59 3.61 3.62 3.63 3.65 3.66 3.67 3.69 3.75

1. State the null and alternative hypothesis.
2. Find the test statistic.
3. State the p-value and interpret.
4. What does the p-value tell us in terms of the null hypothesis?
5. What can we conclude?
6. Calculate a 95% confidence interval and interpret.

1. (12pts) A brochure inviting subscriptions for a new diet program states that the participants are expected to lose at least 22lbs in 5wks. Suppose that, from the data of the 5wk weight losses of 56 participants, the sample mean and standard deviation are found to be 23.4 and 10.1lbs respectively. Are the statements in the brochure correct on the basis of these findings? Use alpha = 0.01 and use the standard error in your calculations (take the sample standard deviation and divide by the square root of the sample size).
   1. State the null and alternative hypothesis.
   2. Find the test statistic.
   3. State the p-value and interpret.
   4. What does the p-value tell us in terms of the null hypothesis?
   5. What can we conclude?
   6. Calculate a 99% confidence interval and interpret.