ANSWER

You would test the equality of variances to see if there is a difference in household income variability between male and female clients. The following are the pertinent hypotheses:

    The null hypothesis (H0) states that the difference in household income between male and female clients is equal.

    Alternative Hypothesis (H1): The difference between the household incomes of male and female clients is more than zero.

The F-test for equality of variances is the appropriate test statistic. At the 0.05 significance level, you compare the derived F-statistic to the crucial F-value. It would be clear that there is a considerable difference in variability if the estimated F-statistic is higher than the crucial F-value.

To conclude, you can compute the F-statistic and determine the critical value using an F-distribution table. You will reject the null hypothesis if the F-statistics associated p-value is less than 0.05.

You can run independent two-sample t-tests for each variable to see any differences between male and female clients for the supplied variables (Income, Average treadmill uses per week, and Average miles per week). Since you are comparing samples of various sizes and do not necessarily assume that the variances are equal, these would be independent two-sample t-tests assuming unequal variances (Welch’s t-test). The following constitutes the test hypotheses:

    To earn money:

        The null hypothesis (H0) states that the mean family income of male and female clients is equal.

        Alternative Hypothesis (H1): Clients who are male do not have clients with median household incomes that are equal to those of clients who are female.

    For typical weekly treadmill usage:

        The null hypothesis (H0) states that the average number of times per week male clients utilize the treadmill is identical to the average for female clients.

        Alternative Hypothesis (H1): Male clients utilize the treadmill on average fewer times per week than female clients.

    The null hypothesis (H0) for average weekly miles is that the mean weekly mileage for male clients is equal to that for female clients.

        Alternative Hypothesis (H1): The median weekly mileage for male clients differs from that for female clients.

Then, compute the p-values by comparing the calculated t-statistics to the critical t-values at the 0.05 significance level. The null hypothesis for that variable will be rejected if the p-value for any of these tests is less than 0.05.

Testing for variances between male and female customers can give the advertising agency helpful information. Effectively modifying advertising campaigns requires understanding the variations between these market segments. The agency can modify its marketing initiatives to more effectively target each gender if substantial variations are discovered in factors like income, use of a treadmill, and weekly miles traveled. For illustration:

    The agency can produce advertisements specifically tailored to the interests and demands of male and female customers by utilizing language and imagery that speaks to each demographic.

    Product Development: The agency might suggest various product features or package deals based on the preferences of different treadmill users or fitness aspirants.

    Pricing Strategies: If there are significant disparities in income, the agency might consider modifying pricing plans or providing payment options that fit each gender group’s budget.

EssentialBy their advertising to the unique features of male and female customers, these studies enable the agency to improve their marketing strategy and maximize the impact of their advertising efforts

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