An airline company is interested in improving customer satisfaction rate from the 72% currently claimed.

Sample Solution

Hypothesis Testing for Customer Satisfaction Rate

Null Hypothesis (H0): The customer satisfaction rate is equal to 72%. Alternative Hypothesis (Ha): The customer satisfaction rate is greater than 72%.

Sample: 300 customers Satisfied Customers: 227

Test Statistic (z):

We can use the one-sample proportion z-test to evaluate the claim.

z = (p̂ - p) / sqrt(p(1-p)/n)

where:

• p̂ (sample proportion) = 227/300 = 0.757
• p (claimed proportion) = 0.72
• n (sample size) = 300

z = (0.757 - 0.72) / sqrt(0.72 * (1-0.72) / 300) = 1.23

P-value:

Using a z-table or calculator, the p-value for z = 1.23 is approximately 0.109.

Full Answer Section

Conclusion:

At a significance level (α) of 0.05, the p-value (0.109) is greater than α. Therefore, we fail to reject the null hypothesis.

Interpretation:

Based on the sample data, we do not have sufficient evidence to conclude that the customer satisfaction rate is higher than 72% at the 5% significance level. We cannot confirm the airline's claim, but we also cannot definitively say the satisfaction rate is lower. It is possible that the observed difference (3.7%) is due to chance, and a larger sample size might be needed to draw a more definitive conclusion.

Additional Notes:

• This analysis only considers a single sample and assumes independence of observations.
• Different significance levels can be used, but the interpretation of the results would change accordingly.