# Hypothesis Testing: Level of Significance and Average Capacities

1. A study has been made to compare the nicotine contents of two brands of cigarettes. Ten cigarettes of Brand A have an average nicotine content of 3.1 milligrams with a standard deviation of .5 milligrams, while 8 cigarettes of Brand B have an average nicotine content on 2.7 milligrams with a standard deviation of .7 milligrams. At a level of significance of .05, test whether the average nicotine between the two brands is different or not.

2. Consider the following data samples on ore capacities of coal from two mines ( in millions of calories per ton);

Mine A : 8,500, 8330, 8,480, 7,960 and 8,030

Mine B: 7,710, 7,890, 7,920, 8,270 and 7,860

Test whether the average ore capacities are the same or not.

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#### Solution Summary

This solution provides guidelines on how to fine the averages of data samples based on different levels of significance.

Statistics 10 problems: Hypothesis test, ANOVA, Chi square, regression, forecasting

See attached file for proper format.

1. [2%] ONE SAMPLE HYPOTHESIS TEST FOR MEAN: A bowler who has averaged 196 pins in the past year is asked to experiment with a ball made of a new kind of material. If he rolls 25 games with the new ball, averaging 204 pins with a standard deviation of 24.9, can one conclude at a level of significance of .01 that the new ball has improved his game?

1a) Direction = UPPER TAILED / LOWER TAILED / 2-TAILED (circle one)

1b) P-value = ________________

1c) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)

1d) Can we conclude the ball improved his game? YES or NO (circle one)

2. [2%] ONE SAMPLE HYPOTHESIS TEST FOR PROPORTION: The Webster University librarian believes that more than 60% of the books checked out by students was fictional material. In a random sample of 1000 students who checked books out in the last year, 628 checked out fictional material. What can one conclude about the librarian's hypothesis at a level of significance of .05?

2a) Direction = UPPER TAILED / LOWER TAILED / 2-TAILED (circle one)

2b) P-value = ________________

2c) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)

2d) Can we conclude the librarian's claim is correct? YES or NO (circle one)

3. [2%] TWO SAMPLE HYPOTHESIS TEST FOR MEAN - INDEPENDENT SAMPLES: Eight college students were randomly divided into 2 groups of 4 each to test whether background music reduces studying capacity. Each person was tasked with memorizing a list of 20 words. Group 1 had music playing through earphones they were wearing. Group 2 was not distracted. The following are the number of words correctly remembered by each subject. Test whether the music reduces studying capacity at a .05 level of significance.

Group 1 -- DISTRACTED Group 2 - NOT DISTRACTED

Sample mean = 7

Sample size = 4

Sample std.dev. = 2.5 Sample mean = 14

Sample size = 4

Sample std.dev. = 3.5

3a) Direction = UPPER TAILED / LOWER TAILED / 2-TAILED (circle one)

3b) P-value = ________________

3c) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)

3d) Can we conclude that music reduces studying capacity? YES or NO (circle one)

4. [2%] TWO SAMPLE HYPOTHESIS TEST FOR PROPORTION: Before starting his campaign for mayor, Mr. Emory Board decided to do a study to see if there was a difference in the proportion of registered men and women voters who actually vote (so he would know whom to target his campaign toward). Of the 100 men and 150 women surveyed, 50 men and 100 women admitted to voting. What can he conclude at the .05 level of significance?

4a) Direction = UPPER TAILED / LOWER TAILED / 2-TAILED (circle one)

4b) P-value = ________________

4c) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)

4d) Can we conclude a difference in voting patterns for men vs. women?

YES or NO (circle one)

5. [2%] TWO SAMPLE HYPOTHESIS TEST FOR PAIRED SAMPLES: In a study of the effectiveness of a reducing diet, the following "before and after" figures (in pounds) were obtained for a sample of 4 adult women in their 30's. What can we conclude from these figures at a level of significance of .01?

Group 1 -- BEFORE Group 2 - AFTER

Woman #1

Woman #2

Woman #3

Woman #4 134

147

178

122 130

140

165

122

5a) Direction = UPPER TAILED / LOWER TAILED / 2-TAILED (circle one)

5b) P-value = ________________

5c) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)

5d) Can we conclude that the diet worked? YES or NO (circle one)

6. [2%] ANOVA: Three groups of 5 students were tested in their ability to correctly answer a 10-question quiz under different formats. Group 1 had a True/False quiz, Group 2 had a Fill-In quiz, and Group 3 had a Multiple Choice quiz. Their scores were as follows:

True/False Fill-In Multiple Choice

6 3 6

8 5 10

9 6 6

7 7 8

10 5 7

Test whether there was a difference in performance on answering the same general questions under different formats. Use a .05 level of significance.

6a) P-value = ________________

6b) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)

6c) Can we conclude a difference in means? YES or NO (circle one)

6d) If the null is rejected, which specific differences are statistically significant?

T/F vs. Fill-in Fill-in vs. Multiple Choice T/F vs. Multiple Choice

(circle all that apply)

7. [2%] CHI SQUARE TEST OF INDEPENDENCE: Of a sample of 80 single and married women surveyed, we obtained the following data as to the sizes of cars each one owns (assuming 1 car per person). Test whether car size is independent of marital status at the .01 significance level.

Compact Midsize Luxury TOTAL

Single 8 14 8 30

Married 32 10 8 50

TOTAL 40 24 16 80

7a) P-value = ________________

7b) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)

7c) Can we conclude that car size is dependent on marital status? YES or NO

(circle one)

8. [3%] CORRELATION & REGRESSION: Dr. A. Nova wanted to test his theory that there was a relationship between one's attendance and one's performance on his Sadistics exams. He tracked the number of days absent for each of his students this term along with their course averages (shown below). Test whether there is a correlation between the two at a .05 significance level. Also use the regression model to predict a student's average if he/she misses 4 classes. BE PREPARED TO ANSWER SIX QUESTIONS REGARDING THE OUTPUT.

Days Absent Course Average

Antonio

Bertram

Cecil

Dudley

Eduardo

Fazzio

Guido

Harvey

Ignatius

Jeremiah 3

1

7

5

0

8

5

3

9

2 85

90

63

78

99

65

80

78

47

88

9. [3%] MULTIPLE LINEAR REGRESSION: Dr. A. Nova conducted a survey to see how well the students performed this semester (measured by their GPA) as a function of their age, gender and course load. The following output shows the first run of multiple linear regression. BE PREPARED TO ANSWER SIX QUESTIONS REGARDING THE OUTPUT. (note: for Gender, 0 = Male, 1 = Female).

10. [3%] FORECASTING: The Surgical Intensive Care Unit would like to be better prepared by forecasting the number of surgical patients they should expect. The past 15 days shows the following numbers of surgeries performed. Conduct a 3-period moving average, an exponential smoothing forecasting using an alpha of .25, and a seasonal forecast with 3 seasons.

Day Surgeries

1 10

2 8

3 12

4 10

5 9

6 14

7 11

8 10

9 15

10 13

11 13

12 16

13 14

14 13

15 18

10a) Forecast for day 16 using 3-period Moving Average = ________________

10b) Forecast for day 16 using Exponential Smoothing (alpha = .25) =________

10c) Forecast for day 16 using Seasonality with 3 seasons = _______________