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Statistics Problem Set #6: Confidence Intervals and Hypothesis Testing, Assignments of Statistics

University of Pennsylvania (UPenn)Statistics

Problem set #6 for statistics 101, which includes various statistical calculations such as finding confidence intervals for means and proportions, determining sample size, and hypothesis testing. The problems involve both normal distribution and binomial distribution.

Typology: Assignments

Pre 2010

Uploaded on 03/28/2010

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Statistics 101 Problem Set # 6
Due: Wednesday December 8th
1. a) Ex 6.96 Page 426
b) Find a 95% confidence interval for (the true mean increase).the true mean increase).
2. a) Ex 6.73 Page 409
b) Ex 6.74 Page 409
3. Four hundred people are surveyed and asked for their opinion on a new TV show on a
scale of 0 (the true mean increase).did not like it at all) to 10 (the true mean increase).really liked it). The following summary information
is given:
Average rating= 7.82
Sample standard deviation = 3.36
The number of individuals that give a score of at least 9: 144 out of the 400.
a) Find a 95% confidence interval for the mean population rating , .
b) Find a 95% confidence interval for the proportion in the population would give
the new TV show a rating of least 9.
4a. Ex 7.24 Page 454
4b. Ex 7.26 Page 455
The data are available on the website as internet.jmp
5a. Ex 8.25 Page 519
5b. How many free throws would Leroy have to shoot if you want the margin of error in
a 95% confidence interval to be .08?
6. When a person is well, the test result for a certain disease is normally distributed with
=10 (the true mean increase).null hypothesis) and =2. For individuals with the disease, the mean test result is
also normally distributed with =15 (the true mean increase).alternative hypothesis) and =2.
We classify a person as not having the disease if the test result does not exceed c and
having the disease if the test result exceeds c. Of course, this classification produces
errors: classifying a non-diseased person as having the disease and a person that has the
disease as not having the disease.
a) What must c have to be if =.05?
b. Based on the value of c in part a) what is the probability of a Type II error?
c. What would be the P-value for a test result of 14?
(over)
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Download Statistics Problem Set #6: Confidence Intervals and Hypothesis Testing and more Assignments Statistics in PDF only on Docsity!

Statistics 101 Problem Set # 6

Due: Wednesday December 8

th

  1. a) Ex 6.96 Page 426 b) Find a 95% confidence interval for  (the true mean increase).the true mean increase).
  2. a) Ex 6.73 Page 409 b) Ex 6.74 Page 409
  3. Four hundred people are surveyed and asked for their opinion on a new TV show on a scale of 0 (the true mean increase).did not like it at all) to 10 (the true mean increase).really liked it). The following summary information is given: Average rating= 7. Sample standard deviation = 3. The number of individuals that give a score of at least 9: 144 out of the 400. a) Find a 95% confidence interval for the mean population rating , . b) Find a 95% confidence interval for the proportion in the population would give the new TV show a rating of least 9. 4a. Ex 7.24 Page 454 4b. Ex 7.26 Page 455 The data are available on the website as internet.jmp 5a. Ex 8.25 Page 519 5b. How many free throws would Leroy have to shoot if you want the margin of error in a 95% confidence interval to be .08?
  4. When a person is well, the test result for a certain disease is normally distributed with =10 (the true mean increase).null hypothesis) and =2. For individuals with the disease, the mean test result is also normally distributed with =15 (the true mean increase).alternative hypothesis) and =2. We classify a person as not having the disease if the test result does not exceed c and having the disease if the test result exceeds c. Of course, this classification produces errors: classifying a non-diseased person as having the disease and a person that has the disease as not having the disease. a) What must c have to be if =.05? b. Based on the value of c in part a) what is the probability of a Type II error? c. What would be the P-value for a test result of 14?

(over)

Extra Credit

It is determined that the mean salary for males working at a given job is M =60K (the true mean increase).thousand). The question is whether females are being discriminated against in terms of salary. To this end, the following test is performed: H 0 : F  60K versus Ha: F < 60K where F denotes the mean for females. Assume that 1. F =20K where F denotes the standard deviation of salaries for females.

  1. A sample of size n females is taken. a. Assume =.05 and n=100. How likely would this test indicate that there is discrimination for the following values of F : 52K; 54K;56K and 58K? b. You need not do the calculations, but would the answers in part a. be higher or lower if  were changed to .01? .10? c. Assume =.05. You need not do the calculations, but would the answers in part a. be higher or lower if n were to changed to 400? 25? d. Assume =.05 and n=10,000. i) Would you reject the number hypothesis if the sample average of female salaries was 59K? ii) What is the P-value for a sample average of 59K? iii) Even if the average female salary was 59K and technically there is dis- crimination, the amount of discrimination of 1K is not that severe. Use this statement to discuss the difference between a hypothesis test that determines whether there is statistical significance or statistical significance and the practical statement that the degree of discrimination in dollar terms is materially significant or insignificant. e. Assume =.05. What would be the smallest sample size that is needed if you want the test to correctly conclude there is discrimination with probability .95 when F is 58K?