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Hypothesis Testing Review Questions

Question 1 Tests for butterfat milk content were performed on milk from a sample of 20 Holstein dairy cows. The sample mean was 3.88% and the standard deviation was .42 percentage points. Test at the 5% significance level whether the data provide sufficient evidence to conclude that the population from which the sample was taken had a mean of 4%.

a. What kind of hypothesis test would you perform? b. State your null hypothesis c. State your alternative hypothesis d. Calculate your test statistic e. What is your critical value? f. What do you conclude?

Question 2 Reports indicate that graduating seniors in a local high school have an average reading comprehension score of 72.55 with a standard deviation of 12.62. As an instructor in a GED course that provides alternative educational opportunities for students, you're curious how seniors in your program compare. Selecting a sample of 25 students from your program and administering the same reading comprehension test, you discover a sample mean of 79.53. State an appropriate null hypothesis to test whether there's a significant difference between the performance of seniors in your program and the seniors in the traditional high school environment. Assume you are working at the .05 significance level.

a. What kind of hypothesis test would you perform? b. State your null hypothesis c. State your alternative hypothesis d. Calculate your test statistic e. What is your critical value? f. What do you conclude?

Question 3 Sally obtains a sample of 78 observations. Assume she is conducting a single sample t test: What would the degrees of freedom be this for this sample?

Question 4 The following null hypothesis is tested: H0: mu = 35.8. Assuming you are conducting a single sample z test, write me a sample problem (we have done this in class) that includes this null hypothesis.

Question 5 Answer the following:

a. What hypothesis is the one we are testing?
b. What hypothesis is our research hypothesis?

Question 6 When two samples of people with something in common are compared with each other, we use the ________________ hypothesis testing procedure.

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Question 1 Tests for butterfat milk content were performed on milk from a sample of 20 Holstein dairy cows. The sample mean was 3.88% and the standard deviation was .42 percentage points. Test at the 5% significance level whether the data provide sufficient evidence to conclude that the population from which the sample was taken had a mean of 4%.

a. What kind of hypothesis test would you perform? Even though the question involves proportions, we are really testing a mean. We will use a one-sample t-test.

b. State your null hypothesis H0: the mean buttermilk content is equal to 4%; μ = 4

c. State your alternative hypothesis Ha: the mean buttermilk content is different from 4%; μ ≠ 4

d. Calculate your test statistic The test statistic is calculated as:

Sx is the sample standard deviation divided by the square root of the number of cases.

t = 3.88 - 4 = -0.12/0.0939 = -1.28
0.42/√20

e. What is your critical value? Find the critical value using a t-distribution table with 19 degrees of freedom. At the 5% level, the critical value is t = ±2.08.

f. What do you conclude? Since -1.28 is NOT less ...

$2.19