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# Hypothesis Testing & Confidence Interval

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1. A machine produces 3-inch nails. A sample of 10 nails was selected and the lengths determined. The results are as follows:
2.89 2.95 3.00 3.05 2.99 2.96 3.10 3.06 3.00 3.12
Use these results to test H0: &#61549; = 3 and Ha: &#61549; &#61625; 3 at &#61537; = 0.01. Give the critical region, the computed test statistic, and the conclusion.

2. A group of people who believe they have psychic abilities are asked to use psychic intuition to deduce the correct sequence of a series of cards. The average score obtained by random guessing alone would be 20 correct out of a standard series of trials. The following are the scores for a sample of psychics: 31, 24, 21, 25, 32. You wish to determine whether your subjects do better, on average, than expected by just guessing.
a. What is the null hypothesis and the alternate hypothesis?
b. What is the criterion (critical) t at alpha = .05?
c. What is your obtained t?
d. Draw final conclusions

3. The number of sit-ups that a person can do in one minute, both before and after a physical fitness course was recorded. The data is shown below for 10 randomly selected participants. Is there sufficient evidence to conclude that a significant amount of improvement took place? Assume variable is normally distributed. Test using &#61537; = 0.01.

Before 30 23 25 29 27 25 30 45 34 26
After 31 27 25 35 34 35 32 52 50 43

4. You are given the following data. Test the claim that there is a difference in the means of the two groups. Use &#61537; = 0.10.

Group A Group B
Xbar 1 = 2 xbar 2 = 1.7
S1= 0.6 s2 = 0.7
N1=120 n2 = 34

5. From your t distribution table, identify the value of t at df = 15:

a. such that only 1% of the t values would be higher
b. such that only 5% of the t values would be lower

6. If alpha is set at .05 and the researcher reports that the t score "approached significance", what is she actually saying? What is the relationship between p and t? Between tobt and tcrit?

7. For a random sample, = 90 and n = 65; assume the standard deviation is 15.

a. Perform a statistical test that compares the sample mean to a population mean of 80. Is it significantly different?

b. Construct a 95% confidence interval for the mean. What does this tell you?

c. If you constructed a confidence interval at 99%, how would that interval compare to the one at 95%? Why?

8. Provide an example of a research question and design that would utilize the statistics for:
a. an independent samples t test
b. a dependent samples t test
c..a one sample t test

9. A research article states the following: "After analyzing the depression scores of adolescents, the mean of 55 for our sample differed significantly from the population mean of 70 for adults, t(45) = 3.76, p < .01."

Identify the following:the n, the statistical test performed and the outcome, the type of error possibly being made, and the alpha that was used.

10. A researcher decides to test whether taking an algebra class immediately prior to enrolling in a statistics class is beneficial. He knows that on a standardized statistics exam, = 68.5. After testing those students who took the algebra class first, he obtained = 78.5 based on 10 students and s2x = 130.42. Assume alpha to be .05.
a. What is tobt?
b. .What is tcrit?