Exam 3

MATH 117 Rose, Fall 2020 Test 3 TR Part 1 will be submitted through WileyPlus, and will be excerpted from your WileyPlus homework. It is timed; you will be allowed 75 minutes and the timing begins once you start this part of your test. This portion of the test should be completed by midnight on Tuesday Nov 24. This deadline reflects the college schedule—there are no classes on Wednesday Nov 25. To ensure you have enough time to complete your test, THIS PORTION OF THE TEST will be available to you at 7 PM on Monday Nov 23. Although the original due date for this part of the test is midnight on Tuesday, all students are given an automatic extension to midnight on Wednesday Nov 25. However, note that no assistance will be available from the instructor after noon on Wednesday Nov 25, so you are encouraged to complete your test by midnight on Tuesday. This document is Part 2 and will be submitted through Blackboard. Your test will be emailed to you at the beginning of class on Tuesday Nov 24. It is due at the end of class and should be submitted in the assignment Submit Test 3 Here in the Test 3 folder. You may type directly on the document OR you may print the document then write on it OR you may handwrite the questions and and answers on a separate page and scan or photograph and upload them. Please upload with a .pdf, doc, docx, jpeg or png file. Other files may not work. If you type into the document, SAVE IT with another name before typing on it, then SAVE IT again before uploading. It is your responsibility to check the document after submitting to make sure it uploaded and is not blank, although I will do my best to check papers as they are turned in. PLEASE check your papers for completeness; I do not have time to do that during the test. The Confidence Interval Upload Assignment due last week was designed to prepare you for the test. Please plan on using the same technology methods you used on the assignment when you complete the test. Note that on this test there are three required screenshots. There is one screenshot required in question 1 and 2 screenshots required for question 2. If you are submitting a document from your phone you must use the Blackboard app. If you have technical issues such as a Wiley crash or difficulty uploading to Blackboard, IT IS YOUR RESPONSIBILITY to notify the instructor BEFORE the test is due. If you are ill or you have other extenuating circumstances that prevent you from taking this test, you must have notifed the instructor BEFORE the test was emailed to you.

The Chapter 6 formula sheet is found at the end of the test.

Good luck on your test!

1. (20 pts)Now that most classes are conducted via Zoom and only a participant’s top half shows to others, students and faculty only need to dress with a shirt or sweater and can wear more comfortable pants such as sweatpants or pajamas that they wouldn’t ordinarily wear to campus. A student who only identifies as StatFiend has surveyed faculty to test if more than half the faculty dress for class. a. If 𝑝𝑝𝑑𝑑 is the proportion of faculty that fully dress for class, state StatFiend’s null and alternative hypotheses, using correct formal notation. b. Results from the sample of 𝑛𝑛 = 127 faculty show that most dress for class. StatFiend uses decides to use the formula in the Chap 6 formula sheet. Are the conditions for using the normal distribution satisfied? Show your work.

Continued

c. Remember that StatFiend is using the Chap 6 formula sheet. What is StatFiend’s standard error? Show the formula, your substitution and any calculations, and rounding to 3 decimal places. d. StatFiend calculates a test statistic of 2.028. Use StatKey to complete the test at the 𝛼𝛼 = 0.05 level of significance. Show your work and conclude if the null hypothesis is rejected or not.

Continued

e. Upload a screenshot of your StatKey graph. f. Interpret the results of the hypothesis test. What evidence does StatFiend have?

2. (10 pts) Log onto StatKey and create two graphs. Graph 1 should be from a distribution N(25, 65), that is a normal distribution with mean 25 and standard deviation 65. Graph 2 should be from a distribution N(35, 45), that is a normal distribution with mean 35 and standard deviation 45.

a. Make a screenshot of each graph and upload each graph. b. Which graph is taller? Explain how you can tell from looking at the graphs on your screen. c. Which graph has a wider 95% interval? Explain how you can tell from looking at the

graphs on your screen. d. Suppose that you didn’t have access to StatKey. How can you tell which graph has a

wider 95% interval? Be specific in your explanation.

3. (15 pts) On the review for this test there was an exercise about daily caloric intake for women. Here is a copy of the exercise:

A rough estimate for the caloric needs of a moderately active female is 2000 calories per day. The Nutrition database contains self-reported data on calorie intake for a sample of 273 women. The sample mean is 1741 calories consumed per day and the sample standard deviation is 620. It appears that this sample of women are consuming fewer calories than recommended. You want to test if the mean caloric intake for all women is reported as significantly less than recommended.

a. The solutions to this question state that this is a left-tail test. What in the question tells you this is a left-tail test? (Please be thorough in your explanation as you have already been given solutions to the original question.)

Continued

b. In this study the sample size was 𝑛𝑛 = 273. Suppose, however that the sample size was only 𝑛𝑛 = 26, so that the sample size was too small to justify using the t-distribution. What other information could possibly be used to satisfy the conditions for using the t-distribution? Explain where you found this information. c. The value of the test statistic for this problem results is a negative number. Suppose that you are unable to complete the test for a p-value and you can only examine the test statistic. What does the negative number tell you? What does the negative number NOT tell you?

Chapter Summaries 743

Chapter 6: Inference for Means and Proportions Under general conditions we can find formulas for the standard errors of sample means, proportions, or their differences. This leads to formulas for computing confi- dence intervals or test statistics based on normal or t-distributions.

Distribution Conditions Standard Error

Proportion Normal np ≥ 10 and n(1 − p) ≥ 10

√ p(1 − p)

n

Mean t, df = n − 1 n ≥ 30 or reasonably normal

s√ n

Difference in Proportions

Normal n1p1 ≥ 10, n1(1 − p1) ≥ 10, and n2p2 ≥ 10, n2(1 − p2) ≥ 10

√ p1(1 − p1)

n1 + p2(1 − p2)

n2

Difference in Means

t, df = the smaller of n1 − 1 and n2 − 1

n1 ≥ 30 or reasonably normal, and n2 ≥ 30 or reasonably normal

√ s2 1

n1 +

s2 2

n2

Paired Difference in Means

t, df = nd − 1 nd ≥ 30 or reasonably normal

sd√ nd

Confidence Interval Test Statistic

General Sample statistic ± z∗ ⋅ SE Sample statistic − Null parameter

SE

Proportion p̂ ± z∗ ⋅ √

p̂(1 − p̂) n

p̂ − p0√ p0(1−p0)

n

Mean x ± t∗ ⋅ s∕ √ n

x − 𝜇0 s∕ √ n

Difference in Proportions

(p̂1 − p̂2) ± z ∗ ⋅

√ p̂1(1 − p̂1)

n1 + p̂2(1 − p̂2)

n2

(p̂1 − p̂2) − 0√ p̂(1−p̂) n1

+ p̂(1−p̂) n2

Difference in Means

(x1 − x2) ± t ∗ ⋅

√ s2 1

n1 +

s2 2

n2

(x1 − x2) − 0√ s2 1

n1 +

s2 2

n2

Paired Diff. in Means

xd ± t ∗ ⋅

sd√ nd

x d − 0

sd∕ √ nd

yields

1. hypotheses:
2. verify:
3. formula:
4. test:
5. evidence:
6. taller:
7. wider:
8. widerAgain:
9. leftTest:
10. justify:
11. negative: