Question

A simple random sample of 10 people shopping at Target found a sample mean age of 27 and a sample standard deviation of 4.27 yrs. Can the market research team definitively declare that the mean age of the population of shoppers at Target is less than 30? Suppose that the level of significance is 0.05.

Answer 1

Solution:

Given:

Claim: the mean age of the population of shoppers at Target is less than 30.

Level of significance = 0.05.

Sample size = n = 10

Sample mean =   years

Sample standard deviation = s = 4.27 years.

Step 1) State H0 and H1:

Vs  

Left tailed test .

Step 2) Test statistic:

Step 3) critical value:

df = n - 1 = 10 - 1 = 9

One tail area = Level of significance = 0.05.

t critical value = -1.833

( critical value is negative, since this left tailed test)

Step 4) Decision Rule:

Reject null hypothesis H0, if t test statistic value < t critical value =-1.833, otherwise we fail to reject H0

Since t test statistic value = < t critical value =-1.833, we reject null hypothesis H0.

Step 5) Conclusion:

At 0.05 level of significance, we have sufficient evidence to support the claim of  the market research team that the mean age of the population of shoppers at Target is less than 30.

Thus the market research team can definitively declare that the mean age of the population of shoppers at Target is less than 30