Question

Dr. Mack Lemore, an expert in consumer behavior, wants to estimate the average amount of money that people spend in thrift shops. He takes a small sample of 8 individuals and asks them to report how much money they had in their pockets the last time they went shopping at a thrift store. Here is the data: 14.95,24.32,27.76,27.37,18.98,11.99,16.66,12.03. He wishes to lest the null hypothesis that the average amount of money people have in their pockets is equal to $20. Calculate the test statistic to two decimal places. Take all calculations toward the answer to three decimal places

Answer 1

To calculate the test statistic for estimating the average amount of money spent in thrift shops, we need the sample mean and standard deviation. The test statistic is then determined using the t-test formula, and the resulting value is compared to the critical value from the t-distribution to decide on the null hypothesis.

Step-by-step explanation:

To calculate the test statistic for Dr. Mack Lemore's study on the average amount of money people spend in thrift shops, we first need to find the sample mean and standard deviation based on the provided data. Let's denote the null hypothesis as H0: μ = $20.

We compute the sample mean (μx) and the sample standard deviation (s) as follows:

1. Compute the sample mean: (μx) = (14.95 + 24.32 + 27.76 + 27.37 + 18.98 + 11.99 + 16.66 + 12.03) / 8
2. Compute each value's deviation from the mean, square these deviations, add them up, and divide by the sample size minus one (n - 1) to get the sample variance (s2).
3. Take the square root of the sample variance to get the sample standard deviation (s).
4. The test statistic (t) is then calculated using the formula: t = (μx - μ0) / (s / √n), where μ0 is the hypothesized population mean ($20) and n is the sample size (8).

Once we have the test statistic, we can compare it with the critical value from the t-distribution to determine whether to reject or not reject the null hypothesis. Note that this process assumes that the sample comes from a normally distributed population and that the sample size is small (n < 30).

The p-value associated with the test statistic would provide the probability of observing a sample mean at least as extreme as the one observed if the null hypothesis were true. Depending on the p-value and the chosen level of significance (α), Dr. Mack Lemore might conclude whether the null hypothesis can be rejected.