Question

An airline company is interested in improving customer satisfaction rate from the 61% currently claimed. The company sponsored a survey of 292 customers and found that 192 customers were satisfied. Determine whether sufficient evidence exists that the customer satisfaction rate is higher than the claim by the company.

What is the test statistic z?

Answer 1

To test if the customer satisfaction rate is higher than the claim, we calculate the z-test statistic using the formula, plugging in the sample proportion, hypothesized population proportion, and sample size.

Step-by-step explanation:

To determine whether there is sufficient evidence that the customer satisfaction rate is higher than the 61% claimed by the airline company, we can use a one-sample z-test for proportions. The test statistic z is calculated using the formula:

z = (p - p0) / sqrt(p0(1 - p0) / n),
where p is the sample proportion, p0 is the hypothesized population proportion, and n is the sample size. In this case, p = 192/292, p0 = 0.61, and n = 292.
Plugging in the numbers, we get:
z = (192/292 - 0.61) / sqrt(0.61(1 - 0.61) / 292)
Once the calculation is done, you will have the direct answer in 2 lines: the value of the z-test statistic. This value can be compared to a critical z-value to make a decision about the null hypothesis.