Statistics college level project ( NO PLAGIARISM )

This chapter is from Introduction to Statistics for Community College Students, 1st Edition, by Matt Teachout, College of the Canyons, Santa Clarita, CA, USA, and is licensed

under a “CC-By” Creative Commons Attribution 4.0 International license – 10/1/18

Practice Problems Section 3B

(#1-20) For each of the following, use the given test statistic and critical value or values to answer the following questions.

a) Draw the indicated distribution and use the critical values to label the tails.

b) Does the test statistic fall in one of the tails or not?

c) Does the sample data significantly disagree with the null hypothesis? Explain how you know.

Tail Test Statistic Critical Value 1 Two Z = 2.47 ±1.96 2 Left T = −3.318 −1.747 3 Right 𝜒𝜒2 = 6.943 12.33 4 Right F = 1.126 3.881 5 Left Z = −1.33 −1.645 6 Two T = 1.994 ±2.738 7 Right 𝜒𝜒2 = 18.441 6.972 8 Right F = 7.509 3.469 9 Two Z = −2.72 ±2.576

10 Left T = −3.871 −2.114 11 Left Z = −1.884 −2.576 12 Right T = 0.472 1.577 13 Two 𝜒𝜒2 = 11.943 2.346 & 9.841 14 Right F = 5.218 2.791 15 Left Z = −2.712 −1.96 16 Two T = 1.138 ±2.005 17 Right 𝜒𝜒2 = 38.644 12.359 18 Right F = 1.528 2.467 19 Left Z = −0.72 −2.576 20 Two T = −2.871 ±2.334

(#21-23) Use the “theoretical distributions” menu in StatKey at www.lock5stat.com to look up the following critical values. Click on the button that says “normal”. Then answer the questions.

21. Z-test statistic = 2.36 Two-tailed test Significance Level = 5% (0.025 in each tail)

Critical Values =

Does the sample data significantly disagree with the null hypothesis? Explain why.

22. Z-test statistic = −1.48 Left-tailed test Significance Level = 1% (0.01 in left tail)

Critical Value =

Does the sample data significantly disagree with the null hypothesis? Explain why.

This chapter is from Introduction to Statistics for Community College Students, 1st Edition, by Matt Teachout, College of the Canyons, Santa Clarita, CA, USA, and is licensed

under a “CC-By” Creative Commons Attribution 4.0 International license – 10/1/18

23. Z-test statistic = 2.02 Right-tailed test Significance Level = 10% (0.10 in right tail)

Critical Value =

Does the sample data significantly disagree with the null hypothesis? Explain why.

(#24-26) Use the “theoretical distributions” menu in StatKey at www.lock5stat.com to look up the following critical values. Click on the button that says “t”. Then answer the questions.

24. T-test statistic = −1.773 Two-tailed test Degrees of Freedom = 29 Significance Level = 1% (0.005 in each tail)

Critical Values =

Does the sample data significantly disagree with the null hypothesis? Explain why.

25. T-test statistic = 2.871 Right-tailed test Degrees of Freedom = 34 Significance Level = 10% (0.10 in right tail)

Critical Value =

Does the sample data significantly disagree with the null hypothesis? Explain why.

26. T-test statistic = −1.144 Left-tailed test Degrees of Freedom = 49 Significance Level = 5% (0.05 in left tail)

Critical Value =

Does the sample data significantly disagree with the null hypothesis? Explain why.

(#27-29) Use the “theoretical distributions” menu in StatKey at www.lock5stat.com to look up the following critical values. Click on the button that says “ 𝜒𝜒2 ”. Then answer the questions.

27. 𝜒𝜒2-test statistic = 38.725 Right-tailed test Degrees of Freedom = 29 Significance Level = 5% (0.05 in right tail)

Critical Value =

Does the sample data significantly disagree with the null hypothesis? Explain why.

28. 𝜒𝜒2-test statistic = 15.846 left-tailed test Degrees of Freedom = 39 Significance Level = 10% (0.10 in left tail)

Critical Value =

Does the sample data significantly disagree with the null hypothesis? Explain why.

This chapter is from Introduction to Statistics for Community College Students, 1st Edition, by Matt Teachout, College of the Canyons, Santa Clarita, CA, USA, and is licensed

under a “CC-By” Creative Commons Attribution 4.0 International license – 10/1/18

29. 𝜒𝜒2-test statistic = 5.119 two-tailed test Degrees of Freedom = 19 Significance Level = 1% (0.005 in each tail)

Critical Value =

Does the sample data significantly disagree with the null hypothesis? Explain why.

(#30-32) Use the following one-population test statistic formula to calculate the one-population proportion Z-test statistic. Then write a sentence to explain the test statistic.

One-Population Proportion Z-Test Statistic = (𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑃𝑃𝑃𝑃𝑃𝑃𝑆𝑆𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃−𝑃𝑃𝑃𝑃𝑆𝑆𝑃𝑃𝑆𝑆𝑆𝑆𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝑃𝑃𝑃𝑃𝑃𝑃𝑆𝑆𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃)

𝑆𝑆𝑃𝑃𝑆𝑆𝑃𝑃𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 𝐸𝐸𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃

30. Sample Proportion (𝑝𝑝𝑝) = 0.317 Population Proportion (𝜋𝜋) = 0.25 Standard Error = 0.031

Z-test statistic =

Test Statistic Sentence:

31. Sample Proportion (𝑝𝑝𝑝) = 0.835 Population Proportion (𝜋𝜋) = 0.9 Standard Error = 0.053

Z-test statistic =

Test Statistic Sentence:

32. Sample Proportion (𝑝𝑝𝑝) = 0.112 Population Proportion (𝜋𝜋) = 0.2 Standard Error = 0.047

Z-test statistic =

Test Statistic Sentence:

(#33-35) Use the following one-population test statistic formula to calculate the one-population mean T-test statistic. Then write a sentence to explain the test statistic.

One-Population Mean T-Test Statistic = (𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑀𝑀𝑆𝑆𝑆𝑆𝑃𝑃−𝑃𝑃𝑃𝑃𝑆𝑆𝑃𝑃𝑆𝑆𝑆𝑆𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝑀𝑀𝑆𝑆𝑆𝑆𝑃𝑃)

𝑆𝑆𝑃𝑃𝑆𝑆𝑃𝑃𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 𝐸𝐸𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃

33. Sample Mean (𝑥𝑥𝑥) = 135.7 mg Population Mean (µ) = 100 mg Standard Error = 23.9 mg

T-test statistic =

Test Statistic Sentence:

This chapter is from Introduction to Statistics for Community College Students, 1st Edition, by Matt Teachout, College of the Canyons, Santa Clarita, CA, USA, and is licensed

under a “CC-By” Creative Commons Attribution 4.0 International license – 10/1/18

34. Sample Mean (𝑥𝑥𝑥) = 89.26 ℉ Population Mean (µ) = 89.6 ℉ Standard Error = 0.108 ℉

T-test statistic =

Test Statistic Sentence:

35. Sample Mean (𝑥𝑥𝑥) = 52.71 thousand dollars Population Mean (µ) = 60 thousand dollars Standard Error = 6.42 thousand dollars

T-test statistic =

Test Statistic Sentence:

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