Question

a software company is interested in improving customer satisfaction rate from the 73% currently claimed. the company sponsored a survey of 199 customers and found that 157 customers were satisfied. what is the test statistic z? ex: 1.23 round z to two decimal places.

Explanation:

Step1: Calculate sample proportion

$\hat{p} = \frac{157}{199} \approx 0.7889$

Step2: Set hypothesized proportion

$p_0 = 0.73$

Step3: Compute standard error

$SE = \sqrt{\frac{p_0(1-p_0)}{n}} = \sqrt{\frac{0.73(1-0.73)}{199}} \approx \sqrt{\frac{0.1971}{199}} \approx 0.0314$

Step4: Calculate z test statistic

$z = \frac{\hat{p} - p_0}{SE} = \frac{0.7889 - 0.73}{0.0314} \approx 1.51$

Answer:

1.51