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Hypothesis Testing & Descriptive Statistics

1. What is the relationship between the value for degrees of freedom and the shape of the t distribution? What happens to the critical value of t for a particular alpha level when df increases in value

2. The following sample was obtained from a population with unknown parameters
Scores: 8, 0, 8, 8
a. Compute the sample mean and standard deviation.
b. Compute the estimated standard error for M.

3. A sample of n=16 individuals is selected from a population with a mean of 78. A treatment is administered to the individuals in the sample and after treatment, the sample variance is found to be s^2 =144.
a. If the treatment has a 4 point effect and produces a sample mean of M=82, is this sufficient to conclude that there is a significant treatment effect using a two-tailed test with alpha=.05?
b. If the treatment has an 8 point effect and produces a sample mean of M=86, is this sufficient to conclude that there is a significant treatment effect using a two=tailed test with alpha=.05?

4. Last fall, a sample of n=25 freshman was selected to participate in a new 4 hour training program designed to improve study skills. To evaluate the effectiveness of the new program, the sample was compared with the rest of the freshman class. All freshmen must take the same English language skills course, and the mean score on the final exam for the entire freshman class was 74. The students in the new program had a mean score of M=78 with SS=2400
a. On the basis of these data, can the college conclude that the students in the new program performed significantly better than the rest of the freshman class? Use a one tailed test with alpha =.05
b. Can the college conclude that the students in the new program are significantly different from the rest of the freshman class? Use a two tailed test with alpha=.05

5. For each of the following situations, assume that mean1=mean2 and calculate how much difference should be expected between the two sample means.
a. One sample has n=8 scores with SS=30 and the second sample has n=8 scores with SS=26.
b. One sample has n=8 scores with SS=150 and the second sample has n=4 scores with SS=90.

6. One sample has n=6 scores with SS=500 and a second sample has n=9 with SS=670.
a. Calculate the pooled variance for the two samples.
b. Calculate the estimated standard error for the sample mean difference.
c. If the sample mean difference is 10 points, is this enough to reject the null hypothesis for an independent measures hypothesis test using alpha =.05? Assume a two tailed test.
d. If the sample mean difference is 15 points, is this enough to reject the null hypothesis for an independent measures hypothesis test using alpha=.05. Assume a two tailed test.

7. When people learn a new task, their performance usually improves when they are tested the next day, but only if they get at least 6 hr of sleep. The following data demonstrate this phenomenon. The participants leaned a visual discrimination task on one day, and then were tested on the task on the following day. Half of the participants were allowed to have at least 6 hr of sleep and other half were kept awake all night. Is there a significant difference between the two conditions? Use a two-tailed test with alpha =.05

6 hr sleep no sleep
N=8 n=8
M=72 M=61
SS=440 SS=456

8. In a classic study of problem solving, Duncker asked participants to mount a candle on a wall in an upright position so that it would burn normally. One group was given a candle, a book of matches, and a book of tacks. A second group was given the same items, except that the tacks and the box were presented separately as two distinct items. The solution to this problem involves using the tacks to mount the box (a shelf) because it was already serving a function (holding tacks) for each participant; the amount of time to solve the problem was recorded. Data similar to Duncker's are as followings

Time to solve problem
Box of tacs tacks and box separate
128 42
160 24
113 68
101 35
94 47

Do the data indicate a significant difference between the two conditions?
Test at the .01 level of significant difference.

Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis and descriptive statistics. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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