Show all of your work on your own paper.
1.
Define level of significance for a hypothesis test.
2.
Define Type I error.
3.
Define Type II error.
4.
For the following state the null hypothesis and alternate hypothesis: The mean number of hours an American spends working is at least 35 hours a week.
5.
Decide whether the following example would be right-tailed, left-tailed or two-tailed: No more than 25% of Americans have blue eyes.
6.
Find the critical value(s) for a right-tailed z-test with α = 0.33
.
7.
Suppose a claim is made that the average GPA of a student at HCC is greater than 2.5.
The mean of a sample of 100 students is found to be 2.6. Explain why the sample mean may not provide enough statistical evidence to support this claim. Answer in a way that shows an understanding of hypothesis testing.
8.
A study claims that the mean weight of 8-year-olds in the U. S. is 50 lb. A sample of sixty 8-year-olds is found to have a mean weight of 51.5 lb and a standard deviation of 5.5 lb.
Use a hypothesis test to analyze the claim with a level of significance of α =
0.05
. (a) State the claim mathematically. (b) State H
0
and H a
and label the claim. (c) Draw a sketch with the rejection region(s) shaded. (d) Find z
0
or t
0
and label the sketch. (e) Compute the test statistic and label the sketch. (f) Make a conclusion about
0
9.
A national study claims the mean life span for an American woman is greater than 80 years. The mean life span of a sample of 20 American women is found to be 83 years with a standard deviation of 5.2 years. Assume that the distribution is normal. Use a hypothesis test to analyze the claim with a level of significance of α =
0.05
. (a) State the claim mathematically.
(b) State H
0
and H a
and label the claim. (c) Draw a sketch with the rejection region(s) shaded.
(d) Find z
0
or t
0
and label the sketch. (e) Compute the test statistic and label the sketch. (f)
Make a conclusion about
0
10.
A recent study claims that 6.3% of Floridians are less than 5 years old. A random selection of 200 Floridians is made and 14 of them are less than 5 years old. Analyze the selection results with a hypothesis test and a level of significance α =
0.01
. (a) State the claim mathematically. (b) State H and H and label the claim. (c) Identify the shape of the
0 a distribution. (d) Compute the test statistic (e) Find the P-value. (f) Make a conclusion about H
0
. (g) Write a conclusion about the claim.
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11.
The correlation between the GPA and starting salaries of 20 recent graduates is found to be 0.55. Use a hypothesis test to decide if there is a significant correlation. Use α
= 0.10
. (a)
State the claim mathematically. (b) State
0 a the rejection region(s) shaded. (d) Find z
0
or t
0
and label the sketch. (e) Compute the test statistic and label the sketch. (f) Make a conclusion about
0 claim.
You may fill in the tables on the test sheet for the last two problems.
12.
Compute the correlation coefficient for the following data from four students. The x values are grades on a Math test and the y values are grades on an English test. x
70
75
85
90 y
75
75
90
95 xy 2 x
2 y x
70
75
85
90
13.
Find a regression line for the same data as problem 12. Also use the regression line to predict the test grade in English of a student who scores an 80 on the Math test. y
75
75
90
95 xy 2 x
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