Question

Question-A cosmetic company claims that its customers spend an average of more than $3,000 a year on makeup. A random sample of 60 customers gave a mean of $3,250 with a standard deviation of $1,620. At ? =0.10, can you conclude than the mean customer spending on makeup is more than $3,000?

Show all steps of the hypothesis test: Hypotheses, Alpha, Distribution, Sketch with Critical Value, Calculate Test Statistic by hand and put on Sketch, Decision, Conclusion.

Answer 1

Sample size = n = 60

Sample mean = = 3250

Standard deviation = s = 1620

Claim: Customers spend an average of more than $3,000 a year on makeup.

The null and alternative hypothesis is

Level of significance = 0.10

Here population standard deviation is unknown so we have to use the t-test statistic.
Test statistic is

Degrees of freedom = n - 1 = 60 - 1 = 59

Critical value = 1.671 ( Using t table)

Test statistic | t | < critical vaue we fail to reject null hypothesis.

Conclusion: Customers does not spend an average of more than $3,000 a year on makeup.