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# Hypothesis testing and confidence interval problems

1. Two teachers give the same standardized statistics test. The results are:

Teacher 1 Mean=75 N=20
Teacher 2 Mean=80 N=15

a. What would be a 95% confidence interval for each of the classes?

b. The true mean for the test is 70, with a standard deviation of 5. Can you draw any conclusions about either of the classes from this information?

c. Is there a significant difference for either class?

2. The probability of getting an item on a test correct, is 0.2. Assume that all items are independent.
a. What is the mean for the distribution of probabilities?

b. On a test with 25 items
i. What is the standard deviation?

ii. What is the probability of having exactly 5 correct answers?

iii. What is the probability of having at least 3 correct answers?

iv. How likely is it that 4 answers would be incorrect?

c. Use the normal approximation for find the probability that if there were 100 items, you would get more than 60 correct.

d. What is the probability that you would get two correct and then two wrong?

3. The pass rate for a test is 60%. A teacher gives the test to 40 students; 75% of them pass.
a. What test would you use to test how well the students did?

b. What is the null hypothesis?

c. Is there a significant difference between the class and the overall group?

4. Greek letters are used in statistics
a. To make it more difficult for students
b. Because the Greeks invented statistics
c. To designate characteristics of populations
d. To designate sample parameters

5. A company institutes new policies to increase job satisfaction. They give a sample of employees a questionnaire to measure job satisfaction, before and after the policies are put into place.
a. 10 employees completed the questionnaire. The average change in their level of satisfaction was 1 out of 100 points, with a standard deviation of 20. What is the p-value?

b. The company then had 1000 employees complete the questionnaire and found that the results were statistically significant. Does this differ from the conclusion in a. Why or why not? As an employee do you think these changes are worthwhile?

#### Solution Preview

Please show solutions and explanations for the questions created for survey
1. Two teachers give the same standardized statistics test. The results are

Teacher 1 Mean=75 N=20
Teacher 2 Mean=80 N=15
a. What would be a 95% confidence interval for each of the classes?
The confidence interval is given by
Details
Teacher 1
Confidence Interval Estimate for the Mean

Data
Population Standard Deviation 5
Sample Mean 75
Sample Size 20
Confidence Level 95%

Intermediate Calculations
Standard Error of the Mean 1.118033989
Z Value -1.95996398
Interval Half Width 2.191306351

Confidence Interval
Interval Lower Limit 72.80869365
Interval Upper Limit 77.19130635
Teacher 2

Confidence Interval Estimate for the Mean

Data
Population Standard Deviation 5
Sample Mean 80
Sample Size 15
Confidence Level 95%

Intermediate Calculations
Standard Error of the Mean 1.290994449
Z Value -1.95996398
Interval Half Width 2.530302624

Confidence Interval
Interval Lower Limit 77.46969738
Interval Upper Limit 82.53030262

b. The true mean for the test is 70, with a standard deviation of 5. Can you draw any conclusions about either of the classes from this information?
The value 70 is out side the confidence interval. Thus we can conclude that the mean score of both classes are different from 70
c. Is there a significant difference for either class?
H0: There is no significant difference in the mean score.
H1: There is significant difference in the mean score.
Test Statistic used ...

#### Solution Summary

The solution provides step by step method for the calculation of test statistic and confidence interval. 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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