Question

For the following exercise assume that all the assumptions required to apply the one-way ANOVA procedure hold true. A clothing store chain is having a sale based on the use of a coupon. The company is interested in knowing whether the wording of the coupon affects the number of units of the product purchased by customers. The company created four coupons for the same product, each with different wording. Four groups of 50 customers each were selected at random. Group 1 received the first version of the coupon; Group 2 received the second version; and so on. The units of the product purchased by each customer were recorded. a. The following ANOVA table contains some of the values from the analysis. Assume that the four populations are normally distributed with equal variances. Find the missing values and complete the ANOVA table. Round your answers to three decimal places, if required. Source of Variation Between Within Total Degrees of Freedom Sum of Squares Mean Square Value of the Test Statistic 74910.580 F = 77665.713 eTextbook and Media b. What are the appropriate null and alternative hypotheses for this analysis? $H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4$, $H_1$: Not all four population means are equal. $H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4$, $H_1$: Not all four population means are equal. $H_0: \mu_1 \ne \mu_2 \ne \mu_3 \ne \mu_4$, $H_1$: All four population means are equal. $H_0: \mu_1 \ne \mu_2 \ne \mu_3 \ne \mu_4$, $H_1$: All four population means are different from each other. $H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4$, $H_1$: All four population means are different from each other. eTextbook and Media c. Using $\alpha = 0.05$, what is your conclusion about the equality of population means for all four coupons? Because the value of the test statistic is than the critical value of F, we the null hypothesis.

For the following exercise assume that all the assumptions required to apply the one-way ANOVA procedure hold true.
A clothing store chain is having a sale based on the use of a coupon. The company is interested in knowing whether the wording of
the coupon affects the number of units of the product purchased by customers. The company created four coupons for the same
product, each with different wording. Four groups of 50 customers each were selected at random. Group 1 received the first version
of the coupon; Group 2 received the second version; and so on. The units of the product purchased by each customer were
recorded.
a. The following ANOVA table contains some of the values from the analysis. Assume that the four populations are normally
distributed with equal variances. Find the missing values and complete the ANOVA table.
Round your answers to three decimal places, if required.
Source of
Variation
Between
Within
Total
Degrees of
Freedom
Sum of
Squares
Mean
Square
Value of the
Test Statistic
74910.580
F =
77665.713
eTextbook and Media
b. What are the appropriate null and alternative hypotheses for this analysis?
$H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4$, $H_1$: Not all four population means are equal.
$H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4$, $H_1$: Not all four population means are equal.
$H_0: \mu_1 \ne \mu_2 \ne \mu_3 \ne \mu_4$, $H_1$: All four population means are equal.
$H_0: \mu_1 \ne \mu_2 \ne \mu_3 \ne \mu_4$, $H_1$: All four population means are different from each other.
$H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4$, $H_1$: All four population means are different from each other.
eTextbook and Media
c. Using $\alpha = 0.05$, what is your conclusion about the equality of population means for all four coupons?
Because the value of the test statistic is
than the critical value of F, we
the null hypothesis.

Added by Jaime G.

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