Use a one-sample z-test.
z = (sample mean - population mean)/(standard deviation divided by the square root of the sample size)
With your data:
z = (38.7 - 40)/(12.5/√50) = ?
Finish the calculation.
Check a z-table at .05 level of significance for a one-tailed test.
If the z-test statistic exceeds the critical value from the z-table, reject the null. If the z-test statistic does not exceed the critical value from the z-table, do not reject the null.
I hope this will help get you started.
A store manager claims that the average age of his customers is less than 40 years old, while the industry average is 40 years old. He asks you to test his thinking. You collect a sample of 50 customers and found that the average age is 38.7. Assuming that the population standard deviation is 12.5 years and using á = 0.05, test your manager's hypothesis. What is your conclusion?
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