statistics test

1) Briefly describe the difference between null hypothesis and alternative hypothesis. (2)

2) What is the difference between a one sample and a two sample test? What do you further have to address if you are drawing on two samples for your test? (2)

3) Which are the two different kinds of mistakes that we can make in a hypothesis test? How do these two probabilities relate, in general? (2)

4) Employees at a firm produce units at a rate of 125 per hour, with a standard deviation of 25 units per hour. A new employee is tested on 40 separate random occasions, and is found to have an average output of 105 units per hour. Does this indicate that the new employee’s output is significantly different (at the 5% level) from the average output in the firm? (2)

5) Based upon collected data, a local car dealer has estimated that the amount spent on extras in cars is normally distributed with an average of $2,200 per customer. She is interested in the question, whether lately, that average may have changed. Data concerning the purchase of extras by the last nine customers shows the following amounts were spent (in $): 2350, 2486, 1935, 1524, 3221, 2489,1790, 1866, and 2247. Test whether the amounts spent on extras have, in fact, changed, or not. (2)

6) Calculate the critical values for a test, for a significance level of 1% and a sample size of 17, for (a) two tail, (b) upper one tail, (c) lower one tail. (1.5)

7) For testing the effectiveness of a drug, 900 subjects receive an oral administration of the drug in question. Another 1000 subjects receive a placebo. What is a suitable null hypothesis in this case?

You can evaluate whether the drug has an effect on the test subjects by using a standardized scale. For the group having received the drug in question (n=900), the mean test score was 9.78, with a standard deviation of 4.05. For the control group (n=1000), the mean test score was 15.10, with a standard deviation of 4.28. At the 0.1% significance level, can you reject your null hypothesis? (2.5)

8) Pollsters try to assess whether the support for a candidate in a regional election differs in different areas. They randomly interview people in urban and rural environments in that region to find an answer to that question. Of 250 people interviewed in urban areas, 135 indicate that they will vote for said candidate. In rural areas, 80 out of 190 people signal their intent to vote for the candidate. At the 5% significance level, do we accept or reject a null hypothesis stating that support for the candidate is not significantly different in different parts of the region in question? (2)

9) A university finance department would like to assess whether travel expenses claimed by members of different departments are significantly different. Having identified two departments that appear to show rather different reimbursement claims, data for these departments over the last calendar year is assessed. Assuming that population expenses are approximately normally distributed, and that population variances are approximately equal, test whether department A’s claims are significantly higher than department B’s claims, at the 5% significance level. (2)

Individual claims, Department A: 156.67, 169.81, 130.74, 158.86, 146.81, 143.69, 155.38, 170.74, 147.28, 157.58, 179.89, 140.67, 154.78, and 154.86.

Individual claims, Department B: 108.21, 142.68, 135.92, 109.10, 110.93, 132.91, 127.16, and 124.94.

10) For the data in question 10), undertake the same test assuming that the population variances are unequal. (2)

11) Out of 22 rats, 13 were fed a high protein diet, the other 9 were fed a low protein diet. Their weights after twelve weeks are

High protein: 134, 146, 104, 119, 124, 161, 107, 83, 113, 129, 97, 101, and 113.

Low protein: 70, 118, 101, 85, 107, 132, 94, 112, and 105.

Formulate a suitable null hypothesis and test it assuming unequal variances for a high protein diet population and a low protein diet population. (significance level: 5%) (2)

12) Show that the t-statistic you calculate to test your null hypothesis of different population means in two samples, will have the same value in cases of equal and unequal population variances if the two samples have the same size (number of observations). (2)

13) Water samples were taken to assess the concentration of trace metals in a body of water; in this case, the concentration of zinc was of interest. Water samples were taken at ten different locations. Does the data suggest differences in the concentration at the bottom (top row) and surface (bottom row)? (Are these samples dependent or independent?) (2)

14) To assess whether studying times among different groups of students vary significantly, members of two different groups were asked about their weekly studying times. Test whether the variances of the two respective populations can be assumed to be the same. (Alpha = 0.05.) (2)

Group 1 (hours per week): 26, 25, 43, 34, 18, 52, 17, 29.

Group 2 (hours per week): 23, 30, 18, 25, 28, 19, 31.

15) What is the statistical power of the test for question 5) (car dealer), if the average has changed, and is, in fact, $2,300 per customer, now? (2)