Example of 1 Proportion

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%.

Choose Stat > Basic Statistics > 1 Proportion.
From the drop-down list, select Summarized data.
In Number of events, enter 87.
In Number of trials, enter 1000.
Select Perform hypothesis test.
In Hypothesized proportion, enter 0.065.
Click OK.

Interpret the results

The null hypothesis states that the proportion of households that make a purchase equals 0.065. Because the p-value is 0.007, 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%.

Descriptive Statistics

N	Event	Sample p	95% CI for p
1000	87	0.087000	(0.070617, 0.106130)

Test

Null hypothesis	H₀: p = 0.065
Alternative hypothesis	H₁: p ≠ 0.065

P-Value
0.007