A researcher wants to know if the mean times (in minutes) that people watch their favorite news station are the same. Suppose that Table 13.24 shows the results of a study.CNNFOXLocal4515721243371868563850602331513522 Table 13.24Assume that all distributions are normal, the three population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05.

Name: A researcher wants to know if the mean times (in minutes) that people
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: A researcher wants to know if the mean times (in minutes) that people watch their favorite news station are the same. Suppose that Table 13.24 shows the results of a study.CNNFOXLocal4515721243371868563850602331513522 Table 13.24Assume that all distr

Null and alternative hypotheses: There are 3 favourite news stations. Denote the true average times the people watch each of their favourite news stations as μ1, μ2, and μ3. The hypotheses to be tested are: Null hypothesis: H0: μ1 = μ2 = μ3. That is, the mean times that people watch their favourite news station are the same. Alternative hypothesis: Ha: At least one of the mean times that people watch their favourite news station is different. Evidently, the test is for equality of 3 means. The means take numerical values. Now, a one-way ANOVA is the most suitable for testing the equality of several means, provided the assumptions of independence of observations, normality of residuals and homogeneity of variances are satisfied.Test statistic and P-value: The test is conducted here by using EXCEL. Software procedure: The step-by-step procedure to conduct the ANOVA test is given below: Enter the data of CNN, FOX, Local in the columns A, B, and C. Select Data > Data Analysis > ANOVA: Single factor > OK. In Input Range enter $A$1:$C$7. In Grouped by select Click on Labels in First Row. Enter Alpha as 05 and click OK. The output using EXCEL is as follows: From the above obtained output below values are reported: The test statistic value is F = 4.0815. From the above obtained output, the P-value is P-value = 0.0401.Decision rule: The level of significance is α = 0.05. Decision rule based on P-value approach: If P-value ≤ α, then reject the null hypothesis H0. If P-value > α, then fail to reject the null hypothesis H0. Conclusion: Conclusion based on P-value approach: The P-value is 0.0401 and α value is 0.05. Here, P-value is less than the α value. That is, 0.0401 (=P-value) < 0.01 (=α). By the rejection rule, reject the null hypothesis. Thus, At least one of the mean times that people watch their favourite news station is different. Hence, there is not enough evidence to support the claim that the mean times that people watch their favourite news station are the same.