A cereal company claims that their “honey and oat" product have a mean weight of 5 ounces following a normal distribution. To test this hypothesis, you select a random sample of 16 bags and find that the mean and standard deviation of this sample are 4.7 ounces and 0.5 ounces, respectively. (a) Use a significance level 0.01 to test the above hypothesis. What is your conclusion? (you need to clearly state the null and alternative hypotheses and show all the necessary steps to get the full score). (b) Illustrate the critical region for the above test.

A study was done on body temperatures of men and women. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Complete parts​ (a) and​ (b) below. Use a 0.01 significance level for both parts. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative​ hypotheses? What is the test​ statistic, t? What is the​ P-value? State the conclusion for the test. b. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.

You are interested in testing whether the average age of household heads is higher in the suburbs than in inner city neighbourhoods. A survey is conducted, and the following results are obtained. In the suburbs, the household heads of the 45 households surveyed had a mean age of 44 with a standard deviation of 15. In the inner city, the mean age of the 40 household heads surveyed was 38 with a standard deviation of 13. Assuming that the populations from which these samples were drawn have equal variances, can you conclude that the difference between the two means is significant at the 95% level of confidence? (a) Write in words and symbols the null and research hypotheses. (b) Assuming the variances of the populations are equal, calculate the value of the Pooled Variance Estimate (PVE). (c) Calculate the value of the standard error for the difference between the two means.

According to a large oil company, the average cost per barrel of oil last year was $47. You believe that due to the current oil crisis in Russia and Iran that the cost of a barrel of oil has decreased. You collect a simple random sample of 60 barrels of oil and find an average price of $42 and a standard deviation of $12. Use this information to answer the following questions and conduct the hypothesis test with a level of significance of a = .01. You may use Statcrunch or a calculator. Write all non-calculation answers in complete sentences. a. Which test would you use and why? b. Write the null and alternative hypothesis in complete sentences. (Make sure you mark which is the null and which is the alternative.) c. Write the null and alternative hypothesis as symbols. d. State the requirements that have been met to run the test. e. What is the test statistic and the p-value? (Make sure you use the right notation.) f. Should you reject or fail to reject the null hypothesis? g. State…