Free Printable Chapter 4

Worksheets

Chapter 4 - STA404

Total questions: 37

Worksheet time: 1hrs 27mins

Name

Class

Date

Is the mean height of female college students greater than 5.5 feet?

Paired t-test. Students heights can be measured against females of similar backgrounds.

1-sample t-test. Test whether the mean of a single sample is equal to the target value of 5.5 feet.

2-sample t-test. Test whether the heights of female college students is higher than their high school heights.

Use a z-test by finding the mean height and standard deviation of the sample of college females' heights.

Does the mean height of female college students significantly differ from the mean height of male college students?

Paired t-test. Test whether the difference of the means of one male paired with one female is equal to 0.

2-sample t-test. Test whether the mean height of female college students is different than the mean height of male college students.

1-sample t-test. Test whether the mean of randomly assigned pairs of female and male students is greater than the mean of the average of males and females.

z-test. Use proportions in place of means to run a one sample z-test for males and females and compare averages.

I run a paired t-test for 15 sets of first grade twins reading abilities if one twin used a computer program tutor and the other did not, and get a p-value of 0.02, what does this mean for a significance level of 0.05?

Reject the null hypothesis. There is evidence at the 0.05 level that the computer program tutor is more effective at raising reading scores.

Fail to reject the null hypothesis. There is no evidence at the 0.05 level that the computer program tutor is more effective at raising reading scores.

Accept the null hypothesis. There is evidence at the 0.05 level that the computer program tutor is more effective at raising reading scores.

This was not the proper use of a paired t-test; no conclusions can be drawn from this test.

We use a paired t-test for 18 students in the Bethel AP statistics class and 18 students in the Kecoughtan class to see if one teacher has higher scores on the AP exam than another.We get a p-value of 0.14. What should we conclude?

Reject the null hypothesis. There is evidence at the 0.05 level that the one teacher has higher scores than another.

Fail to reject the null hypothesis. There is no evidence at the 0.05 level that one teacher has higher scores than another.

Accept the null hypothesis. There is evidence at the 0.05 level that one teacher's scores are higher than the other teacher's.

This was not the proper use of a paired t-test; no conclusions can be drawn from this test.

A manufacturer of gloves wants to determine if a special type of wool gloves lasts longer than the cotton gloves they manufacture. He makes pairs of gloves in which the left hand is cotton and the right hand is wool. We sample 24 women who wear these pairs of gloves, then use a paired t-test to find the mean of the differences in wear between the right glove and left glove; we get a p-value of 0.043. At the 0.05 level, what should we conclude?

Reject the null. There is evidence at the 0.05 significance level that the wool gloves lasts longer than the cotton glove.

Fail to reject the null. There is evidence at the 0.05 significance level that the wool glove lasts longer than the cotton glove.

Fail to reject the null. There is no evidence at the 0.05 significance level that the wool glove lasts longer than the cotton glove.

We cannot conclude anything because a paired t-test was not the appropriate test to run for this sample.

A researcher gave one group of people an active drug and gave a different group of people an inactive placebo, then compare the blood pressures between the groups. Which test should he run to determine the efficacy of the active drug?

Paired t-test. Since there is a group with the active drug and another with the inactive drug, he may pair the two two groups if the sample sizes are the same.

2-sample t-test. Since the blood pressures were taken for patients in sample 1 and different patients in sample 2, use a two-sample t-test to see if the results are statistically significant.

1-sample t-test. The researcher should compare the mean of the first sample of patients to the mean of the second sample of patients.

2-sample z-test. There is no natural pairing between the two samples, so the researcher must use a proportions test.

Which one is NOT a related design

Independent groups design

Repeated measures design

Matched pairs design

A test for an association (difference or correlation). Data is nominal using an unrelated design

Chi Squared

Mann Whitney

Related t-test

Unrelated t-test

What is the key difference between one-way ANOVA and a t-test?

You can have more than 2 groups in ANOVA

They are the same test just with different calculations

T-tests split variance into within and between

ANOVA is about the mean and t-test is about the variance

10.

What does ANOVA stand for?

Analysis of Variation

Analysis of Variance

Analyzing Ordinal Variation

At Northern Virginia

11.

Which group is causing the differences here?

High Stress

Moderate Stress

Low Stress

They all contribute equally

12.

A tire manufacturer claims that one particular type of tire will last at least 50,000 miles. A group of angry customers does not believe this is so. They take a sample of 14 tires to test if the mean mileage of the tires is really less than 50,000. What set of hypotheses are they interested in testing?

a) H0: m = 50,000 vs. Ha: m < 50,000

b)H0: x̅ = 50,000 vs. Ha: x̅ < 50,000

c)H0: m = 50,000 vs. Ha: m ≠ 50,000

d)H0: m = 50,000 vs. Ha: m > 50,000

13.

A tire manufacturer claims that one particular type of tire will last at least 50,000 miles. A group of angry customers does not believe this is so. They took a sample of 14 tires to test if the mean mileage of the tires is really less than 50,000. If 0.0100 < P-value < 0.0200, what decision should be made if testing at the a = 0.05 level?

a)Reject H0 and conclude that the tires were not performing as claimed.

b)Reject H0 and conclude that the mean tire life really is 50,000 miles.

c)Do not reject H0 and conclude that the tires were not performing as claimed.

d)Do not reject H0 and conclude that the mean tire life really is 50,000 miles.

14.

Does South Lake Tahoe have the same ethnic makeup as that of the (known) distribution of California? Five Hundred South Lake Tahoe residents were asked about their ethnicity.

one sample mean interval

one sample proportion test

chi square test

linear regression test

15.

The Mean of a set of data is represented by which Greek letter?

beta

alpha

16.

A study is done to see how chocolate affects weight in women. They given each woman 2 ounces of chocolate each day and monitor their weight each week for 6 months. What is the response variable?

Weight

Chocolate

6 months

2 ounces

17.

ANOVA is used to compare the differences in _________ for more than 2 populations

variances

means

regression

18.

With p-value approach, the H₀will rejected if p-value is ________ than α

≤

≥

19.

What is the key difference between one-way ANOVA and a t-test?

You can have more than 2 groups in ANOVA

They are the same test just with different calculations

T-tests split variance into within and between

ANOVA is about the mean and t-test is about the variance

20.

A survey of 280 homeless persons showed that 63 were veterans. Construct a 90% confidence interval for the proportion of homeless persons who are veterans.

(0.161 to .289)

(0.176 to 0.274)

(0.184 to 0.266)

(0.167 to 0.283)

21.

The 90% interval for a statistics test was given by 72 +- 7. What is the lower value for the interval?

22.

Which of the following is NOT a parameter?

p̂

23.

A mayor is concerned about the percentage of city residents who express disapproval of his job performance. His political committee pays for a newspaper ad, hoping to keep his disapproval rating below 21%. They will use a follow up poll to assess effectiveness. What are the correct null and alternative hypotheses?

Ho: p=.21
Ha: p > .21

Ho: p< .21
Ha: p= .21

Ho: p> .21
Ha: p= .21

Ho: p= .21
Ha: p< .21

24.

Agricultural researchers plant 100 plots with a new variety of corn and measure the mean yield for these plots in bushels per acre. They treat the 100 plots as a simple random sample of possible plots of corn (as researchers often do) and report a 95% confidence interval for the mean corn yield of (128.4, 131.6) bushels per acre. Which of the following is a correct interpretation of the 95% confidence level?

We are 95% confident that the true mean yield for this new variety of corn is captured by the interval (128.4, 131.6) bushels per acre

If many intervals were constructed this way from many independent sets of 100 plots, 95% of the intervals would capture the true mean corn yield.

If many intervals were constructed this way from many independent sets of 100 plots, 95% of the time the true mean corn yield would be in the interval (128.4, 131.6) bushels per acre.

25.

The National Park Service compared the average amount of money spent by visitors in two different national parks. They sampled visitors on the same day in each of the two parks. What type of problem is this?

Matched Pairs

Two independent samples

26.

Many people believe that playing chess can have a positive effect on reading ability. A sample of n = 53 students was chosen. They participated in a comprehensive chess program, after which they were given a reading test. What is the correct t* for a 90% confidence interval for the true mean reading score?

a)1.645

b)1.671

c)1.676

d)2.009

27.

9 randomly sampled students were asked how many hours of TV they watched last week. x̅ was 3.5 h and s was 4 h. For 95% confidence and 8 degrees of freedom, t*=2.3. The stem plot was somewhat skewed to the right, with no outliers. What is the 95% conf. int. for m?

a)3.5 ± (2.3×4)

b)3.5 ± (2.3×4 / 9)

c)3.5 ± (2.3×4×9)

d)3.5 ± (2.3×4 / 3)

28.

A student wanted to assess the average time spent studying for his most recent exam taken in class. He asked the first 45 students who came to class how much time they spent and recorded the values. He then used this information to calculate a 95% confidence interval for the mean time spent by all students. Was this an appropriate use of the t procedure for a confidence interval?

a)Yes, because we can assume that the time spent studying was normally distributed.

b)Yes, because the 45 students is a big enough sample to invoke the CLT.

c)No, because time spent studying is not a quantitative variable.

d)No, because there was no randomization in choosing the sample.

29.

Each of 16 milk cows were fed 2 diets in random order. Milk production was measured for each of the cows while being fed each of the 2 diets so that 32 milk production values were recorded. Matched pairs one-sample t-procedures will be used for inferences. How many degrees of freedom does the applicable t-distribution have?

30.

Would I use the z-test or t-test and why?

Z-test, n > 30

T-test, n < 30

31.

Would I use the z-test or t-test and why?

Z-test, n > 30

T-test, n < 30

32.

Would I use the z-test or t-test?

Z-test

T-test

33.

Would I use the z-test or t-test?

Z-test

T-test

34.

Use the z-table to calculate the critical value.

z_o = 1.28

z_o = 1.03

35.

Use the z-table to calculate the critical value.

z_o = 1.03

z_o = -1.28

36.

Use the z-table to calculate the critical values.

z_o = -1.96 and 1.96

z_o = -1.45 and 1.45

37.

In 1882 Michelson tried to estimate the speed of light. He reported the results of 23 randomly selected trials with a mean of 756.22 km/sec. It is known that the actual speed of light is 300,000 km/sec with a distribution that is approximately Normal and sigma = 107.12 km/sec. Was Michelson's calculation significantly lower than the acual speed of light?

z test for means

t test for means

z test for means, but Not Normal

t test for means, but Not Normal

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Chapter 4 - STA404

Total questions: 37

Worksheet time: 1hrs 27mins

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