Question

A store manager claims that 60% of shoppers who enter her store make a purchase. To investigate this claim, she selects a random sample of 40 customers and finds that 40% of them make a purchase. She wants to know if the data provide convincing evidence that the true proportion of all customers entering her store who make a purchase differs from 60%. What are the values of the test statistic and P-value for this test?

Answer 1

The test statistic is -1.33 and the P-value is approximately 0.183.

Step-by-step explanation:

To test whether the data provides convincing evidence that the true proportion of all customers entering the store who make a purchase differs from 60%, we need to perform a hypothesis test.

Let's define the null hypothesis (H0) as the proportion of shoppers who make a purchase is equal to 60%, and the alternative hypothesis (Ha) as the proportion is different from 60%.

Step 1: Find the test statistic

We have a sample proportion of 40% (0.40) out of 40 customers, which means X = 0.40 * 40 = 16.

To find the test statistic, we use the formula:

test statistic = (sample proportion - hypothesized proportion) / sqrt((hypothesized proportion * (1 - hypothesized proportion)) / sample size)

test statistic = (0.40 - 0.60) / sqrt((0.60 * (1 - 0.60)) / 40) = -1.33

Step 2: Find the P-value

The P-value is the probability of observing a test statistic as extreme as the one calculated if the null hypothesis is true.

We can find the P-value by looking up the test statistic (-1.33) in a standard normal distribution table or using a statistical software. The P-value is approximately 0.183.