The marketing manager for a home mobility aids needed more information about the age profile of potential customers. The manager predicts that the average age of customers is greater than 70 years. A random sample of 25 customers is selected from various retirement villages and their age (in years) is recorded. This data is located in Sheet A of the Practice Data fileIs there sufficient evidence to support the manager’s claim? Use 0.05 level of significance.The hypothesis to test this claim is
Question
The marketing manager for a home mobility aids needed more information about the age profile of potential customers. The manager predicts that the average age of customers is greater than 70 years. A random sample of 25 customers is selected from various retirement villages and their age (in years) is recorded. This data is located in Sheet A of the Practice Data fileIs there sufficient evidence to support the manager’s claim? Use 0.05 level of significance.The hypothesis to test this claim is
Solution
To test the manager's claim, we would use a one-sample t-test. Here are the steps:
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State the Hypotheses: The null hypothesis (H0) would be that the average age of customers is 70 years. The alternative hypothesis (H1) would be that the average age of customers is greater than 70 years.
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Choose the Significance Level: The significance level is given as 0.05.
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Calculate the Test Statistic: Using the data from Sheet A of the Practice Data file, calculate the sample mean and standard deviation. Then, calculate the test statistic using the formula for a one-sample t-test.
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Determine the Critical Value and Rejection Region: Since this is a one-tailed test (we are only interested if the average age is greater than 70), the critical value and rejection region will be determined from the t-distribution table using degrees of freedom (n-1) and the significance level.
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Make a Decision: If the test statistic falls in the rejection region, reject the null hypothesis in favor of the alternative. This would provide sufficient evidence to support the manager's claim. If the test statistic does not fall in the rejection region, there is not enough evidence to support the claim.
Remember,
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