Question

A store owner daims the average age of her customes is 33 vean. 5 he took a survey of 37 randomly selected customers and found the sveragt age to be 35.5 years aith a stanifacd errec of 1.121 . Carry out a typothesis test to determine if her ctaim is redwonoble. (a) Wrich hypotheres should be tected? (b) Find the teit statistie: (Use 4 decimals.) (c) What is the p-value? (Use 4 decimali.) (d) What shauld the vore ewner concluce, for a =0.05 ? the inctal elaim of 33 years. There is evisence the aveage customer age is 3.. (0) it mean oulomer age redil is equat to 33 yean, but you conclude it is dererent than 33 yeack, which type of enter did you make, if any? Thpe 1 error Tyell ereor Both Type t and Type 11 error Nó errer nas made

Answer 1

To determine if the store owner's claim is reasonable, we need to conduct a hypothesis test. The null hypothesis (H0) is that the average age of the customers is 33 years, while the alternative hypothesis (Ha) is that the average age is different from 33 years.

Step-by-step explanation:

To determine if the store owner's claim is reasonable, we need to conduct a hypothesis test. The null hypothesis (H0) is that the average age of the customers is 33 years, while the alternative hypothesis (Ha) is that the average age is different from 33 years.

To find the test statistic, we can use the formula:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Using the given values, we can calculate the test statistic as follows:

t = (35.5 - 33) / (1.121 / sqrt(37))

Calculating this expression gives us the test statistic: t = 4.9720.

The p-value can be calculated by finding the probability of observing a test statistic as extreme or more than the one calculated. This can be done using a t-distribution table or a statistical calculator.

For a significance level of 0.05, the critical value is 1.96 for a two-tailed test. Since the test statistic (4.9720) is greater than the critical value, we reject the null hypothesis. This means that there is evidence to suggest that the average customer age is different from 33 years.

In this case, a Type 1 error was made. A Type 1 error occurs when the null hypothesis is rejected even though it is true.