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A researcher conducts an independent-measures study comparing two treatments and reports the t statistics as t(25)= 2.071.
How many individuals participated in the entire study?
use a two tailed test with o=.05 and the distributions tool below to determine if there is significant difference between the two treatments.
* Reject the null hypothesis; there is no significant difference
* Fail to reject the null hypotheses; there is no significant difference.
* Reject the null hypothesis, there is a significant difference
* Fail to reject the null hypothesis; there is a significant difference.
Compute r2 to measure the percentage of variance accounted for by the treatment effect.
The number of individuals participated in the entire study = 27
t-critical= +/- 2.060
Reject the null hypothesis, there is a significant difference
r2 = 14.6%
Here, the degrees of freedom of the test is given to be 25.
For an ...
The solution explains the determination of sample size, critical value and percentage of variance accounted for by the treatment effect for a independent sample t test.
Statistics Problems: Test for mean, proportion, paired samples, independence
See attached file for clarity of the tables included.
1. 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. ONE SAMPLE HYPOTHESIS TEST FOR PROPORTION: The Trinity 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. 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. 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. 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 #4 134
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. 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. 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
8. 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 geography 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.
Days Absent Course Average
9. 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.
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 = _______________