Question

Study on teenager spending habits stated that the average amount teens spend on apparel each year is $655. If a

random sample of 45 teens reported that they spent on average $663 on apparel last year, assuming o = $19, at
a = 0.05, can it be concluded that the average amount they spent on apparel was not equal to $655?
Hypothesis:

Answer 1

To determine if the average amount teenagers spent on apparel was not equal to $655, a hypothesis test can be conducted using a t-test. Calculating the t-value and comparing it to the critical t-value at a significance level of 0.05 will help determine if the null hypothesis should be rejected.

Step-by-step explanation:

To test whether the average amount teenagers spent on apparel was not equal to $655, we can conduct a hypothesis test. Our null hypothesis (H0) is that the average amount they spent on apparel is $655, and the alternative hypothesis (Ha) is that the average amount is not equal to $655. With a random sample of 45 teens and a known population standard deviation of $19, we can use a t-test.

We calculate the test statistic using the formula:
t = (sample mean - population mean) / (population standard deviation / sqrt(sample size))
Plugging in the values, we get:
t = (663 - 655) / (19 / sqrt(45))

Next, we compare the calculated t-value to the critical t-value at a significance level of 0.05, with (45 - 1) degrees of freedom. If the calculated t-value falls outside the critical t-value range, we reject the null hypothesis and conclude that the average amount teenagers spent on apparel was not equal to $655.