# Regression ,Hypotheses testing and confidence intervals

1. Scores on a statistics test are normally distributed with a mean of 80 and a SD of 5. The average for a class of 30 is 90. The teacher of that class says that her class has done significantly better than average.

a. What null hypothesis would you use to test the teacher's statement?

b. What is the mean and the standard deviation of the distribution you would use to test that hypothesis?

c. What is the p-value? What conclusion can you draw from it?

2. You have 10 gifts; they include 2 dolls, 2 trucks, 3 books, and 3 balls. Children are asked to choose a gift, without knowing what they are choosing.

a. What is the probability that the first child picks a truck and the second picks a doll?

b. What is the probability that the first child picks a book or a doll?

3. Calculate the area for the following values of X, when the mean is 10 and the standard deviation is 2.

a. P(X<8)

b. P(X>14)

c. P(8<X<14)

4. As your sample size increases

a. the p-value will increase

b. the mean will increase

c. the standard deviation will decrease

d. the chance of accepting the null hypothesis will increase

5. Explain the two types of mistakes you can make in hypothesis testing. Give an example when you would be more concerned about one than the other.

.

6. X has a uniform distribution between 0 and 4.

a. Draw the distribution.

b. Find P(X< 2)

c. What is P( 3<X<4)?

7. The following table includes men's and women's records in the 800-meter run in selected years.

Year Men's Women's record

1905 113.4 ---

1915 111.9 ----

1925 111.9 144.0

1935 109.7 135.6

1945 106.6 132.0

1955 105.7 125.0

1965 104.3 118.0

1975 104.1 117.5

1985 101.73 113.28

1995 101.73 113.28

a. Do a scatter plot of time, depending on years (this will be easier if you use only the last two digits of the year, e.g. 05, 15, 25,...) for both men and women.

b. Describe the plots. Are there any outliers? Is there a difference between the men and the women?

c. Find the equations for both sets of data.

d. What do expect the times to be in the year 2010?

8. A machine bottling soda overfills bottles 0.1% of the time. An inspector watches a sample of bottles and finds that the machine overfilled 5 out of 1000 bottles.

a. Is there a reason to believe the machine is not working correctly?

b. What is a 95% confidence interval for the sample value of p (5 in 1000, or 0.5%)?

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1. Scores on a statistics test are normally distributed with a mean of 80 and a SD of 5. The average for a class of 30 is 90. The teacher of that class says that her class has done significantly better than average.

a. What null hypothesis would you use to test the teacher's statement?

H0: Mean score ≤ 80

H1: Mean Score >80

b. What is the mean and the standard deviation of the distribution you would use to test that hypothesis?

Mean = population mean =80

Standard deviation = =5/ = 0.9128

c. What is the p-value? What conclusion can you draw from it?

The test statistic is given by

Decision rule: Reject the null hypothesis if the p value is less than 0.05

Details

Z Test of Hypothesis for the Mean

Data

Null Hypothesis = 80

Level of Significance 0.05

Population Standard Deviation 5

Sample Size 30

Sample Mean 90

Intermediate Calculations

Standard Error of the Mean 0.912870929

Z Test Statistic 10.95445115

Upper-Tail Test

Upper Critical Value 1.644853627

p-Value 0.0000

Reject the null hypothesis

Conclusion: Reject the null hypothesis as the p value is less than 0.05. The sample provides enough evidence to support the claim that the mean score in the class is greater 80.

2. You have 10 gifts; they include 2 dolls, 2 trucks, 3 books, and 3 balls. Children are asked to choose a gift, without knowing what they are choosing.

a. What is the probability that the first child picks a truck and the second picks a doll?

Let A be the event that the child picks a ...

#### Solution Summary

The solution provides step by step method for the calculation of Regression equation ,Hypotheses testing and confidence intervals . 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.

Regression Coefficient Tests and Confidence Intervals

Please answer the following questions:

(a) Explain why a confidence interval for the slope or intercept would be equivalent to a two-tailed hypothesis test.

(b) Why is it especially important to test for a zero slope?

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