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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Textbook Question
Chapter 11.9, Problem 12E
Refer to the data of Exercise 11.7.
- a. Calculate a 95% confidence interval for β1.
- b. What is the interpretation of H0: β1 = 0 in Exercise 11.7?
- c. Test the hypotheses H0: β1 = 0 versus Ha: β1 ≠ 0.
- d. Determine the p-value of the test of H0: β1 = 0.
11.7 A food processor was receiving complaints from its customers about the firmness of its canned sweet potatoes. The firm’s research scientist decided to conduct an experiment to determine if adding pectin to the sweet potatoes might result in a product with a more desirable firmness. The experiment was designed using three concentrations of pectin (by weight)–1%, 2%, and 3%–and a control with 0%. The processor packed 12 cans with sweet potatoes with a 25% (by weight) sugar solution. Three cans were randomly assigned to each of the pectin concentrations with the appropriate percentage of pectin added to the sugar syrup. The cans were scaled and placed in a 25°C environment for 30 days. At the end of the storage time, the cans were opened, and a firmness determination was made for the contents of each can. These appear below:
- a. Let x denote the pectin concentration of the sweet potatoes in a can and y denote the firmness reading following the 30 days of storage at 25°C. Plot the sample data in a
scatter diagram . - b. Obtain the least-squares estimates for the parameters, and plot the least-squares line on your scatter diagram.
- c. Does firmness appear to be in a constant increasing relation with pectin concentration?
- d. Predict the firmness of a can of sweet potatoes treated with a 1.5% concentration of pectin (by weight) after 30 days of storage at 25°C.
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Students have asked these similar questions
It is hard to persuade consumers to abandon a product with which they are familiar. One experiment gave consumers free samples of new laundry detergent and also a standard detergent. After some time, ask the subjects which detergent they prefer. Here are the data.
User
Nonuser
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19
31
Prefer standard product
29
27
a. Calculate a 90% confidence interval for the difference in proportions between nonusers and users of the standard detergent that prefer the new detergent.
b. Based on the confidence interval in (a), can we conclude that a significant difference exists between the proportion of nonusers of the standard detergent who prefer the new detergent and the proportion of users of the standard detergent who prefer the new detergent? Explain.
Test the claim that the mean GPA of night students is significantly different than the mean GPA of day students at the 0.05 significance level.The null and alternative hypothesis would be:
H0:pN=pDH0:pN=pDH1:pN≠pDH1:pN≠pD
H0:pN=pDH0:pN=pDH1:pN<pDH1:pN<pD
H0:pN=pDH0:pN=pDH1:pN>pDH1:pN>pD
H0:μN=μDH0:μN=μDH1:μN>μDH1:μN>μD
H0:μN=μDH0:μN=μDH1:μN≠μDH1:μN≠μD
H0:μN=μDH0:μN=μDH1:μN<μDH1:μN<μD
The test is:
two-tailed
right-tailed
left-tailed
The sample consisted of 70 night students, with a sample mean GPA of 3.4 and a standard deviation of 0.03, and 55 day students, with a sample mean GPA of 3.43 and a standard deviation of 0.07.The test statistic is: (to 2 decimals)The positive critical value is: (to 2 decimals)Based on this we:
Fail to reject the null hypothesis
Reject the null hypothesis
Is there sufficient evidence to indicate the overall model is statistically useful for predicting y. Test using α=10%. Make sure you include, in your answer, the null and alternative hypotheses, the value of an appropriate test statistic, the p-value AND rejection region, and conclusion.
Find the 95% confidence interval for β3. Use the interval to determine if mood scores would be useful to the model if both intrapersonal and stress management scores are already included in the model and give a brief explanation.
TestH0: β2=0 against H0: β2>0 at α=05. Make sure you include, in your answer, the value of an appropriate test statistic, p-value AND rejection region, and conclusion.
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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- Test the claim that the mean GPA of night students is significantly different than 2.4 at the 0.2 significance level.The null and alternative hypotheses would be: H0:p=0.6H0:p=0.6H1:p≠0.6H1:p≠0.6 H0:μ=2.4H0:μ=2.4H1:μ≠2.4H1:μ≠2.4 H0:μ=2.4H0:μ=2.4H1:μ>2.4H1:μ>2.4 H0:p=0.6H0:p=0.6H1:p<0.6H1:p<0.6 H0:μ=2.4H0:μ=2.4H1:μ<2.4H1:μ<2.4 H0:p=0.6H0:p=0.6H1:p>0.6H1:p>0.6 The test is: right-tailed left-tailed two-tailed Based on a sample of 31 people, the sample mean GPA was 2.36 with a standard deviation of 0.16The p-value is: (to 3 decimals)The positive significance level is: (to 2 decimals)Based on this we: Reject the null hypothesis Fail to reject the null hypothesisarrow_forwardTest the claim that the mean GPA of night students is significantly different than 2.2 at the 0.1 significance level. The null and alternative hypothesis would be: Ho:p = 0.55 Ho:p = 0.55 Ho: H = 2.2 Ho:p = 0.55 Ho:µ = 2.2 Ho:µ = 2.2 H1:p 2.2 H1:p > 0.55 H1:µ#2.2 H1:µ < 2.2 The test is: right-tailed two-tailed left-tailed Based on a sample of 65 people, the sample mean GPA was 2.21 with a standard deviation of 0.02 The test statistic is: (to 2 decimals) The positive critical value is: (to 2 decimals) Based on this we: OReject the null hypothesis O Fail to reject the null hypothesisarrow_forward
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