An Introduction to Statistical Methods and Data Analysis
7th Edition
ISBN: 9781305269477
Author: R. Lyman Ott, Micheal T. Longnecker
Publisher: Cengage Learning
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Follow the steps to calculate the Independent t-test and conduct a 2-tailed test with a = .05.
Step 1: State both hypotheses (H statements):
Ho: HA = HB
%3D
H, :XA Xg
Ho: HA = Hg
H : XA XB
O Ho: A = B
H: A B
Step 2: State your level of risk:
3.
.50
.05
.01
.10
2.
Question 12
Step 3: What test statistic will you solve for?
Homogeneous t-test
Pearson's t-test
Independent t-test
Dependent t-test
a. What are the sample estimates of β0,β1,and β2?
b. What is the least squares prediction equation?
c. FindSSE,MSE,and standard deviation . Interpret the standard deviation in the context of the problem.
d. Test H0: β1=0 against Ha: β1≠0.Use α=0.01.
e. Use a 95% confidence interval to estimate β2.
f. Find R2 and R^2_a and interpret these values.
g. Find the test statistic for testing H0: β1=β2=0.
h. Find the observed significance level of the test in part g.interpret the result.
A market research firm used a sample of individuals to rate the purchase potential of a particular product before and after the individuals
saw a new television commercial about the product. The purchase potential ratings were based on a 0 to 10 scale, with higher values
indicating a higher purchase potential. The null hypothesis stated that the mean rating "after" would be less than or equal to the mean
rating "before." Rejection of this hypothesis would show that the commercial improved the mean purchase potential rating. Use α = 0.05
and the following data to test the hypothesis and comment on the value of the commercial.
Ha:
a: Md is greater than 0
What are the hypotheses?
Ho: Md is less than or equal to 0
Compute to 3 decimals).
Individual
Compute Sd (to 1 decimal).
1
2
3
4
Purchase Rating
Before
After
6
6
8
5
5
LO
5
8
3
Individual
What is the p-value?
The p-value is between 0.10 and 0.20
What is your decision?
Cannot conclude seeing the commercial improves the mean potential to…
Chapter 11 Solutions
An Introduction to Statistical Methods and Data Analysis
Ch. 11.9 - Prob. 1ECh. 11.9 - Refer to Exercise 11.1.
Plot the equation in the...Ch. 11.9 - Use the data given here to answer the following...Ch. 11.9 - Prob. 4ECh. 11.9 - Use the output from Minitab for these data to...Ch. 11.9 - A food processor was receiving complaints from its...Ch. 11.9 - An online retailer needs to manage the amount of...Ch. 11.9 - A manufacturer of cases for sound equipment...Ch. 11.9 - Refer to the data of Exercise 11.7. a. Calculate a...Ch. 11.9 - Refer to the data of Exercise 11.8.
Calculate a...
Ch. 11.9 - Refer to the data of Exercise 11.8.
Calculate a...Ch. 11.9 - Athletes are constantly seeking measures of the...Ch. 11.9 - A firm that prints automobile bumper stickers...Ch. 11.9 - A chemist is interested in determining the weight...Ch. 11.9 - Refer to Exercise 11.22 to complete the following....Ch. 11.9 - Prob. 40ECh. 11.9 - A survey of MBA, graduates of a business school...Ch. 11.9 - Refer to the data in Exercise 11.44.
Determine the...Ch. 11.9 - There has been an increasing emphasis in recent...Ch. 11.9 - An air conditioning company responds to calls...Ch. 11.9 - Refer to Exercise 11.61. a. Calculate the...Ch. 11.9 - Refer to Exercise 11.61.
Test for lack of fit for...Ch. 11.9 - Refer to Exercise 11.61.
Compute the standard...Ch. 11.9 - Prob. 93SE
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- A market research firm used a sample of individuals to rate the purchase potential of a particular product before and after the individuals saw a new television commercial about the product. The purchase potential ratings were based on a 0 to 10 scale, with higher values indicating a higher purchase potential. The null hypothesis stated that the mean rating "after" would be less than or equal to the mean rating "before." Rejection of this hypothesis would show that the commercial improved the mean purchase potential rating. Use α = 0.05 and the following data to test the hypothesis and comment on the value of the commercial. What are the hypotheses? Ho: dis - Select your answer - H₂: Hd is-Select your answer - Compute a (to 3 decimals). Compute & (to 1 decimal). What is the p-value? The p-value is - Select your answer - What is your decision? - Select your answer - Individual 1 2 3 4 Purchase Rating Before 5 4 After 7 6 8 5 8 3 Individual 5 6 7 8 Purchase Rating Before 4 After 3 9 6 6…arrow_forwardA market research firm used a sample of individuals to rate the purchase potential of a particular product before and after the individuals saw a new television commercial about the product. The purchase potential ratings were based on a 0 to 10 scale, with higher values indicating a higher purchase potential. The null hypothesis stated that the mean rating "after" would be less than or equal to the mean rating "before." Rejection of this hypothesis would show that the commercial improved the mean purchase potential rating. Use α = 0.05 and the following data to test the hypothesis and comment on the value of the commercial. Individual O Ho: Md ≤0 Ha: Md = 0 O Ho: Md ≤0 Ha: Md > 0 O Ho: Md = 0 1 Ha: Md 0 2 3 4 5 6 7 8 Purchase Rating After Before 6 6 7 4 3 7 6 5 4 8 3 State the null and alternative hypotheses. (Use μ = mean rating after - mean rating before.) O Ho: μg 0 Ha: Md = 0 7 8 5 7 Ho: Md > O Ha: Md ≤ 0 Calculate the value of the test statistic. (Round your answer to three…arrow_forwardAn HR manager in a company wants to know if there’s a difference in the amount of timeworkers in different departments spend chatting at the water cooler. She tracks the behaviour for twodepartments (Legal Department and Technical Support) and records the number of minutes spent at thewater cooler for each employee. The data are presented below.Is there a significant difference in time spent at the water cooler between the two departments? Conducta hypothesis test using α = .05. Legal Tech Supportn = 4 n = 8M = 22.2 M = 13.8SS = 164 SS = 76arrow_forward
- 8.38 Speeding and young drivers. Psychologists conducted a survey of 258 student drivers and their attitudes toward speeding and reported the results in the British Journal of Educational Psychology (Vol. 80, 2010). One of the variables of interest was the response to the question, “Are you confident that you can resist your friends’ persuasion to drive faster?” Each response was measured on a 7-point scale, from 1=“definitely no” to7=“definitely yes.” The data were collected 5 months after the students had attended a safe-driver presentation. The psychologists reported a sample mean response of 4.98 and a sample standard deviation of 1.62. Suppose it is known that the true mean response of students who do not attend a safe-driver presentation is μ=4.7.Set up the null and alternative hypotheses for testing whether the true mean student-driver response 5 months after a safe-driver presentation is larger than 4.7.Calculate the test statistic for the hypothesis test.Find the rejection…arrow_forward5.75 Binge drinking. The Centers for Disease Control and Prevention finds that 28% of people aged 18 to 24 years binge drank. Those who binge drank averaged 9.3 drinks per episode and 4.2 episodes per month. The study took a sample of over 18,000 people aged 18 to 24 years, so the population proportion of people who binge drank is very close to p = 0.28.23 The administration of your college surveys an SRS of 200 students and finds that 56 binge drink. (a) What is the sample proportion of students at your college who binge drink? (b) If, in fact, the proportion of all students on your campus who binge drink is the same as the national 28%, what is the probability that the proportion in an SRS of 200 students is as large or larger than the result of the administration's sample? (c) A writer for the student paper says that the percent of students who binge brink is higher on your campus than nationally. Write a short letter to the editor explaining why the survey does not support this…arrow_forwardData from the Motor Vehicle Department indicate that 80% of all licensed drivers are older than age 25. In a sample of n=50 people who recently received speeding tickets, 33 were older than 25 years and the other 17 were age 25 or younger. Is the age distribution for this sample significantly different from the distribution for the population of licensed drivers? Use alpha=0.5. A. what is the proposed analysis and why you chose this? B. Test assumptions and make a decision with evidence? C. Inferential statics and P values? D. Final decision and Conclusion?arrow_forward
- An enzyme immunoassay for the detection of Chlamydia trachomatis in cervical specimens has a sensitivity of 75% and a specificity of 98% when compared with culture. This test will be used by an HMO to screen women of reproductive age who are receiving their annual examination. A previous study, which used culture to screen 1000 women, determined that the prevalence of infection was 2%. In this population, which of the following is the predictive value of a positive screening test? a. 98% b. 75% c. 40% d. 2%arrow_forwardA researcher is examining whether daily yoga reduces stress. The researcher assigns n = 7 individuals to engage in daily yoga for three months and finds an average stress score of M = 16 with SS = 123 after three months for individuals in this group. A second group of n = 6 individuals assigned to a control group for the three months had a stress score of M = 21 with SS = 141. Which of the following is most consistent with the results of conducting a one-tailed independent-measures t test with α = .05? a. t = -1.83 and fail to reject the null hypothesis b. t = -1.83 and reject the null hypothesis c. t = -1.61 and fail to reject the null hypothesid. s t = -1.61 and reject the null hypothesisarrow_forward
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