Question

A company hopes to improve customer​ satisfaction, setting as a goal no more than 9 ​% negative comments. A random survey of 320 customers found only 15 with complaints. ​a) Create a​ two-sided 95 ​% confidence interval for the true level of dissatisfaction among customers. ​b) Does this provide evidence that the company has reached its​ goal? Using your confidence​ interval, test an appropriate hypothesis and state your conclusion. ​a) The 95 ​% confidence interval for the true level of dissatisfaction among customers is left parenthesis nothing comma nothing right parenthesis . ​(Round to three decimal places as​ needed.) ​b) What are the null and alternative​ hypotheses? H0​: p ▼ equals not equals greater than less than nothing vs. HA​: p ▼ equals greater than not equals less than nothing ​(Type integers or decimals. Do not​ round.) Use the confidence interval in part a to draw a conclusion. There ▼ is insufficient is sufficient evidence that the true level of dissatisfaction among customers is less than nothing ​% because nothing is ▼ within the limits above the upper limit below the lower limit of the interval. ​(Type integers or decimals. Do not​ round.) Enter your answer in each of the answer boxes.

Answer 1

(a)

We need to construct the 95% confidence interval for the population proportion. We have been provided with the following information about the number of favorable cases:

Favorable Cases X =	15
Sample Size N =	320

The sample proportion is computed as follows, based on the sample sizeN=320 and the number of favorable cases X=15:

The critical value for α=0.05 is . The corresponding confidence interval is computed as shown below:

b)

a). ​The 95 ​% confidence interval for the true level of dissatisfaction among customers is (0.024,0.07)

b)

H0​: p equals 0.09

vs.

HA​: p less than 0.09

There is sufficient evidence that the true level of dissatisfaction among customers is less than 9​% because 9% is above the upper limit of the interval.
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