A marketing analyst wants to determine whether mailed advertisements for a new product result in a response rate different from the national average. A random sample of 1000 households is chosen to receive advertisements. Of the 1000 households sampled, 87 make a purchase after receiving the advertisement.
The analyst performs a 1 proportion test to determine whether the proportion of households that made a purchase is different from the national average of 6.5%.
The null hypothesis states that the proportion of households that make a purchase equals 0.065. Because the p-value is 0.008, which is less than the significance level of 0.05, the analyst rejects the null hypothesis. The results indicate that the proportion of households that make a purchase is different from the national average of 6.5%.
|N||Event||Sample p||95% CI for p|
|Null hypothesis||H₀: p = 0.065|
|Alternative hypothesis||H₁: p ≠ 0.065|