Final answer:
To determine if there is sufficient evidence that the customer satisfaction rate is higher than the claim by the company, a hypothesis test can be conducted using a significance level of 0.01. The test statistic (z-score) is calculated to be 1.842 and the p-value is approximately 0.0656. Since the p-value is greater than the significance level, there is not enough evidence to reject the null hypothesis.
Step-by-step explanation:
To test whether there is sufficient evidence that the customer satisfaction rate is higher than the claim by the company, we can use a hypothesis test.
Step 1: Formulate the hypotheses:
- Null Hypothesis (H0): The customer satisfaction rate is equal to or lower than the claim by the company (p ≤ 0.69).
- Alternative Hypothesis (Ha): The customer satisfaction rate is higher than the claim by the company (p > 0.69).
Step 2: Calculate the test statistic:
- The test statistic for comparing proportions in this case is the z-score.
- The formula for the z-score is: z = (p - P) / sqrt((P*(1-P))/n), where p is the sample proportion, P is the population proportion, and n is the sample size.
- In this case, p = 121/162 = 0.746, P = 0.69, and n = 162. Plugging these values into the formula gives us: z = (0.746 - 0.69) / sqrt((0.69*(1-0.69))/162) = 1.842.
Step 3: Determine the p-value:
- The p-value is the probability of obtaining a test statistic as extreme as the observed, assuming the null hypothesis is true.
- To find the p-value, we can use a standard normal distribution table or a calculator. The p-value for a z-score of 1.842 is approximately 0.0656.
Step 4: Make a decision:
- Since the p-value (0.0656) is greater than the significance level (a = 0.01), we do not have sufficient evidence to reject the null hypothesis.
- Therefore, we do not have sufficient evidence to conclude that the customer satisfaction rate is higher than the claim by the company.