Question

. As businesses try to survive in the current crisis, Route 22 Honda sought to estimate the satisfaction score from 915 who have purchased a car or truck in 2019.  The company goal is to achieve an average satisfaction score of at least 80 on a scale of 0-100. A random sample of 80 customers had an average satisfaction score of 82.7 and a sample deviation of 6.7

a.       Construct a 95% confidence interval to estimate the actual average satisfaction score form customers in 2019.

b.      Based on this sample, can the manager conclude that Route 22 Honda reached its goal?

2.       2. The state of Florida wanted to estimate the proportion of voters who intend to vote in the presidential election.  A pilot sample of 50 voters found that 36 of them intend to vote in the election. Determine the additional number of voters that need to be sampled to construct a 95% interval with a margin of error equal to 0.05 to estimate the proportion.

3.      3. Apple claims that the average wait time for a customer calling Apple Care support line is 175 seconds.  A random sample of 40 customers had an average wait time of 187 seconds.  Assume the population standard deviation for wait time is 50 seconds

a.       Using a 95% confidence interval, does this sample support Apple’s claim?

Answer 1

n = Sample size = 80

Sample mean =

Sample standard deviation = s = 6.7

Here population standard deviation is not known, but sample size n is large.

So we use z interval.

a) Confidence level = c = 0.95

95% Confidence interval to estimate the actual average satisfaction score form customers in 2019 is

where zc is z critical value for (1+c)/ 2 =(1+0.95) / 2 = 0.975

zc = 1.96 (From statistical table of z values)

(Round to 1 decimal)

95% Confidence interval to estimate the actual average satisfaction score form customers in 2019 is (81.2, 84.2)

b)

Here we have to test that

Confidence interval does not contain null value 80.

So we reject H0.

Conclusion: The manager conclude that Route 22 Honda reached its goal.