A researcher developed a regression model to predict the cost of a meal based on the summated rating (sum of ratings for food, decor,and service) and the cost per meal for 12 restaurants. The results of the study show that b1=1.4379 and Sb1=0.1397. a. At the 0.05 level of significance, is there evidence of a linear relationship between the summated rating of a restaurant and the cost of a meal? b. Construct a 95% confidence interval estimate of the population slope, β1. a. Determine the hypotheses for the test. Choose the correct answer below. A. H0: β1=0 H1: β1≠0 B. H0: β0≤0 H1: β0>0 C. H0: β1≤0 H1: β1>0 D. H0: β0≥0 H1: β0<0 E. H0: β1≥0 H1: β1<0 F. H0: β0=0 H1: β0≠0 Compute the test statistic. The test statistic is ? (Round to two decimal places as needed.) Determine the critical value(s). The critical value(s) is(are) ? (Use a comma to separate answers as needed. Round to two decimal places as needed.) Reach a decision. ▼ Reject Do not reject H0. There is ▼ insufficient sufficient evidence at the 0.05 level of significance to conclude that there is a linear relationship between the summated rating and the cost of a meal at a restaurant. b. The 95% confidence interval is ?≤β1≤?. (Round to four decimal places as needed.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 2AGP

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Question

A researcher developed a regression model to predict the cost of a meal based on the summated rating (sum of ratings for food, decor,and service) and the cost per meal for 12 restaurants. The results of the study show that

b1=1.4379 and Sb1=0.1397.

a. At the 0.05 level of significance, is there evidence of a linear relationship between the summated rating of a restaurant and the cost of a meal?

b. Construct a 95% confidence interval estimate of the population slope,

β1.

a. Determine the hypotheses for the test. Choose the correct answer below.

H0:

β1=0

H1:

β1≠0

H0:

β0≤0

H1:

β0>0

H0:

β1≤0

H1:

β1>0

H0:

β0≥0

H1:

β0<0

H0:

β1≥0

H1:

β1<0

H0:

β0=0

H1:

β0≠0

Compute the test statistic.

The test statistic is ?

(Round to two decimal places as needed.)

Determine the critical value(s).

The critical value(s) is(are) ?

(Use a comma to separate answers as needed. Round to two decimal places as needed.)

Reach a decision.

▼

Reject

Do not reject

H0.

There is

▼

insufficient

sufficient

evidence at the 0.05 level of significance to conclude that there is a linear relationship between the summated rating and the cost of a meal at a restaurant.

b. The 95% confidence interval is

?≤β1≤?.

(Round to four decimal places as needed.)

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