Question

A manufacturer produces smartwatches that have a mean life of at least 200 hours when the production process is working properly. Based on past experience, it is known that the population standard deviation is 25 hours and the smartwatch life is normally distributed. The operations manager selects a random sample of 25 smartwatches, and the mean life of smartwatchers is recorded. d. State the appropriate test used and reason. Determine the appropriate test statistic. Keep at least 2 decimal places. (Hint: for calculating the test statistic, consider the sample mean value from the random sample you have found above)

Appropriate test used and reason:

Test Statistic

e. Find the critical value(s) of the test statistic at the 0.05 level of significance. Keep at least 2 decimal places.

Critical Value

f. Based on your answer in part e, is there evidence that the population mean life of smartwatches is different from 200 hours (use α = 0.05)? Explain by providing the decision and conclusion.

g. Compute the p-value and interpret its meaning under the condition that the null hypothesis is true. Keep at least 4 decimal places.

p-Value

h. Construct a 95% confidence interval estimate for the population mean life of smartwatches. Fill in the table below. Keep at least 4 decimal places. Interpret the meaning of the 95% confidence interval estimates for the population mean when we do not know the population mean. (Hint: consider the interpretation of C.I. in Ch.8)

Confidence Interval (C.I.)

Interval Lower Limit

Interval Upper Limit

i. Based on your answer in part h, what conclusions do you reach? That is, is there evidence that the population mean life of smartwatches is different from 200 hours? Explain by providing your decision and reason for your decision.

Answer 1

(d) The test statistic, z = (x - µ)/σ/√n

z = (210 - 200)/25/√25

z = 2

(e) -1.645

(f) Since the p-value (0.0455) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the population mean life of smartwatches is different from 200 hours.

(g) The p-value is 0.0455.

(h)

200.20	confidence interval 95.% lower
219.80	confidence interval 95.% upper

(i) Yes, since 200 is not in the confidence einterval.

Thanks!