Advanced Statistics Final Review Prep Questions

Statistics practice for final

 

 

Be sure to review the following and have this information handy when taking Final GHA:

 

· Calculating z alpha/2 and t alpha/2 on Tables II and IV

· Find sample size for estimating population mean. Formula 8.3 p. 321 OCR.

· Stating H0 and H1 claims about variation and about the mean. Chapter 9 OCR.

· Type I and Type II errors p. 345 OCR.

· Confidence Interval for difference between two population means. Chapter 10 OCR p. 428

· Pooled sample standard deviation. Chapter 10 OCR p. 397

· What do Chi-Square tests measure? How are their degrees of freedom calculated? Chapter 12 OCR

· Find F test statistic using One-Way ANOVA.xls Be sure to enable editing and change values to match your problem. One-Way ANOVA.xls

· Find equation of regression line used to predict. To do on Excel, go to a blank worksheet, enter x values in one column and their matching y values in another column. Click Insert – Select Scatterplot. Right click any one of the points (diamonds) on the graph. Left click “Add a Trendline.” Check “Display Equation on Chart” box. Regression equation will appear on chart. Try it here with No. 20 below.

 

 

 

Practice Problems

 

Chapter 8 Final Review

1) In which of the following situations is it reasonable to use the z-interval

procedure to obtain a confidence interval for the population mean?

Assume that the population standard deviation is known.

A. n = 10, the data contain no outliers, the variable under consideration is

not normally distributed.

B. n = 10, the variable under consideration is normally distributed.

C. n = 18, the data contain no outliers, the variable under consideration is

far from being normally distributed.

D. n = 18, the data contain outliers, the variable under consideration is

normally distributed.

 

 

 

Find the necessary sample size.

2) The weekly earnings of students in one age group are normally

distributed with a standard deviation of 10 dollars. A researcher wishes to

estimate the mean weekly earnings of students in this age group. Find the

sample size needed to assure with 95 percent confidence that the sample

mean will not differ from the population mean by more than 2 dollars.

 

 

 

Find the specified t-value.

3) For a t-curve with df = 6, find the two t-values that divide the area under

the curve into a middle 0.99 area and two outside areas of 0.005.

 

 

 

 

Provide an appropriate response.

4) Under what conditions would you choose to use the t-interval procedure

instead of the z-interval procedure in order to obtain a confidence

interval for a population mean? What conditions must be satisfied in

order to use the t-interval procedure?

 

 

 

 

CHAPTER 8 Answers

 

1) B

2) 97

3) -3.707, 3.707

4) When the population standard deviation is unknown, the t-interval procedure is used instead of the

z-interval procedure. The t-interval procedure works provided that the population is normally

distributed or the sample is large.

 

Chapter 9 Final Review

 

 

Classify the hypothesis test as two-tailed, left-tailed, or right-tailed.

5) In the past, the mean running time for a certain type of flashlight battery

has been 8.1 hours. The manufacturer has introduced a change in the

production method and wants to perform a hypothesis test to determine

whether the mean running time has changed as a result.

 

Classify the conclusion of the hypothesis test as a Type I error, a Type II error, or a correct decision.

6) The maximum acceptable level of a certain toxic chemical in vegetables

has been set at 0.2 parts per million (ppm). A consumer health group

measured the level of the chemical in a random sample of tomatoes

obtained from one producer to determine whether the mean level of the

chemical in these tomatoes exceeds the recommended limit.

The hypotheses are

H0 : μ = 0.2 ppm

Ha : μ > 0.2 ppm

where μ is the mean level of the chemical in tomatoes from this producer.

Suppose that the results of the sampling lead to nonrejection of the null

hypothesis. Classify that conclusion as a Type I error, a Type II error, or a

correct decision, if in fact the mean level of the chemical in these tomatoes

is greater than 0.2 ppm.

 

Provide an appropriate response.

7) Robert is conducting a hypothesis test concerning a population mean. The

hypotheses are as follows.

H0 : μ = 50

Ha : μ > 50

He selects a sample of size 35 and finds that the sample mean is 60. He

then does some calculations and finds that for samples of size 35, the

standard deviation of the sample means is 3.2. Do you think that he

should reject the null hypothesis? Why or why not?

 

 

The significance level and P-value of a hypothesis test are given. Decide whether the null hypothesis

should be rejected.

8) α = 0.01, P-value = 0.002 5

 

 

Use a table of t-values to estimate the P-value for the specified one-mean t-test.

9) Two-tailed test, n = 9, t = 3.696

 

 

 

Provide an appropriate response.

10) A hypothesis test for a population mean is to be performed. True or false:

The probability of a Type I error is equal to the significance level.

 

 

 

CHAPTER 9 Answers

5) Two-tailed

6) Type II error

7) Answers will vary. Possible answer. Yes, he should reject the null hypothesis. If H0 were true, it is

not very likely that the sample mean would be as big as 60, since this is more than three standard

deviations from 50. So the observed sample mean is inconsistent with the null hypothesis.

 

8) Reject the null hypothesis.

9) P < 0.01

10) True

 

 

Chapter 10 Final Review.

 

 

Summary statistics are given for independent simple random samples from two populations. Use the

pooled t-interval procedure to obtain the specified confidence interval.

11) x1 = 12.8, s1 = 4.1, n1 = 14, x2 = 17.4, s2 = 4.8, n2 = 17

Determine a 95% confidence interval.

 

 

Summary statistics are given for independent simple random samples from two populations. Use the

pooled t-test to conduct the required hypothesis test.

12) x1 = 12.5, s1 = 4.1, n1 = 14, x2 = 16.9, s2 = 4.6, n2 = 17

Perform a two-tailed hypothesis test using a significance level of α = 0.05.

 

 

 

 

Provide an appropriate response.

13) In comparing the means of two populations, some methods are based on

independent samples and some are based on paired samples. Explain the

difference between independent and paired samples. Give an example of

each type of sample.

 

 

 

 

 

CHAPTER 10 Answers

 

11) -7.92 to -1.28

12) Test statistic: t = -2.782

Critical value = ±2.045

Reject H 0

13) In paired samples, there is a natural pairing of the members of the two populations. In independent

samples, no such pairing exists. An example of an independent sample is the income of men and

women. An example of a paired sample is the income of husbands and their wives. (Examples will

vary.)

 

 

Chapter 12 Final Review

 

Use the chi-square table to find the required χ2-value(s).

14) For a χ2-curve with 23 degrees of freedom, find the χ2-value having

area 0.995 to its right.

 

 

15) For a χ2-curve with df = 5, determine χ 2

0.995.

 

 

Perform the required chi-square hypothesis test. Preliminary data analyses and other information

indicate that it is reasonable to assume that the variable under consideration is normally distributed.

Use the critical-value approach or the P-value approach as indicated.

16) In 2000, the standard deviation of the scores of all students taking a

particular test was 20.3. In 2005, the standard deviation of the scores of a

random sample of 18 students taking the same test was s = 27.1. At the

5% level of significance, do the data provide sufficient evidence to

conclude that the standard deviation, σ, of all 2005 scores is different

from the 2000 standard deviation of 20.3? Use the P-value approach.

 

 

 

CHAPTER 12 Answers

14) 9.260

15) 0.412

16) H0: σ = 20.3 Ha: σ ≠ 20.3

α = 0.05

Test statistic: χ2 = 30.297

0.02 < P < 0.05

Reject the null hypothesis. At the 5% level of significance, the data provide sufficient evidence to

conclude that the standard deviation, σ, of all 2005 scores is different from 20.3.

 

 

 

Chapter 13 Final Review

 

Find the required F-value.

17) An F-curve has df = (30, 12). Find the F-value having area 0.01 to its

right.

 

Provide an appropriate response.

18) True or false: In a one-way ANOVA, if the null hypothesis is rejected, we

conclude that the population means are all different (i.e., no two of the

population means are equal).

 

 

 

 

 

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one -way

ANOVA satisfied. Perform the required hypothesis test using the critical value approach.

19) At the 0.025 significance level, do the data provide sufficient evidence to

conclude that a difference exists between the population means of the

four different brands? The sample data are given below. Use One-Way ANOVA.xls. Click Enable Editing and change values to match values in this problem. One-Way ANOVA.xls