What is the Null Hypothesis that the mean Waist Size

Assignment Task

1. To test the null hypothesis that the mean waist size for males under 40 equals 34 versus the hypothesis that the mean differs from 34, the following data were collected:

33, 33, 30, 34, 34, 40, 35, 35, 32,

34, 32, 35, 32, 32, 34, 36, 30, 38

2. At the 0.05 level of significance, analyse the data and write your conclusion. The null hypothesis being tested is “a coin is fair” and the alternative hypothesis is “the coin favors heads.” Let p be the probability of a head occurring. The null hypothesis is H, p=0.5, and the alternative is H , p >0.5. The test statistic, x, is the number ofheads to occur ina set of 12 tosses of this coin. Determine the largest critical region for which aα does not exceed 0.05, by using a discrete variable. (Determine what values of x form the critical region, and state the corresponding value of α.).

3. If two independent random samples (each of size 50) are selected from a standard normal! distribution, explain (show) the probability that the sample means are within 0.5 units of one another.

4. Suppose two independent samples ofequal size are selected from two populations and both having σ = 10, justify what common sample size is needed so that x₁ - x₂ has a standard error equal to 2?

5. A test concerning some of the fundamental facts about AIDS was administered to two groups, one consisting of college graduates and the other consisting of high school graduates. A summary oftest results follows:

College graduates: n=100  x=805  s=6.5

High school graduates: n=100  x =53.4  s=10.7

a. Test at the 0.05 level of significance whether the two sets of scores are equally variable or whether college graduates’ scores are less variable than high school  graduate’ scores. What assumption(s) are necessary?
b. Based on your conclusion in (i), would you pool the sample variances or not? Explain.

c. Do these data show that the college graduates, on the average, score significantly higher on the test? Test the hypothesis using α= 0.05.

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