Assignment: Advance Statistics

Topic : Hypothesis Testing

1.The high school football coach is asked if the players are doing as well academically as the other student athletes. From a previous study the average GPA for the student athletes is 3.10. After an initiative to help improve the GPA of student athletes, the football coach randomly samples 20 football players and finds that the average GPA of the sample is 3.18 with a sample standard deviation of 0.54. Is there a significant improvement? Use a 0.05 significance level.

2.Test whether the mean of a random sample 16 is statistically significantly less than 10 if the distribution from which the sample was taken is normal, mean = 8.4 and variance = 24. What are the null and alternative hypotheses for this test? (at the alpha= .05 significance level)

3.As a baker you know from experience that the standard deviation of the weight of 10lbs packages of cookies is 0.20 lbs. To check whether the true average is, on a given day, 10 pounds, you select a random sample of 36 packages and find that their mean weight is 9.45 lbs. Perform a two-tailed z-test on this data, checking at the alpha= .01 significance level.

4.We compare the yearly income of a designer in Baguio and Manila, two cities in the Philippines. It is known from experience that the variance of yearly incomes in Baguio is40,000 and the variance for yearly incomes in Manila is90,000. A random sample of 20 families was taken in Baguio, yielding a mean yearly income of47,000, while a random sample of 30 families was taken in Manila, yielding a mean yearly income of52,000. At the alpha= .01 significance level, test whether or not there is a significant different in average yearly income between the two cities.

5.The vacuum cleaner company stated that a unit expends 46 kWh per year. A random sample of 12 homes indicates that vacuum cleaners expend an average of 42 kWh per year with (sample) standard deviation 11.9 kWh. At a 0.05 level of significance, does this suggest that, on average, vacuum cleaner expend less than 46 kWh per year? Assume the population to be normally distributed.

6.A flyer inviting subscriptions for a new workout program states that the participants are expected to lose over 22 pounds in five weeks. Suppose that, from the data of the five-week weight losses of 56 participants, the sample mean and sample standard deviation are found to be 23.5 and 10.2, respectively. Could the statement in the brochure be substantiated on the basis of these findings? Test at the alpha= .05 level

7.The mean systolic blood pressure of 157 half-Filipino men, was 146 mm Hg with a standard deviation of 27. We wish to know if on the basis of these data, we may conclude that the mean systolic blood pressure for a population of half-Filipino is greater than 140. Use =0.01.

8.Eveready manufactures batteries that the CEO claims will last an average of 300 hours under normal use. A researcher randomly selected 20 batteries from the production line and tested these batteries. The tested batteries had a mean life span of 270 hours with a standard deviation of 50 hours. Do we have enough evidence to suggest that the claim of an average lifetime of 300 hours is false? Use a 0.05 significance level