Question

The average income of American women who work full-time and have only a high school diploma is $31,666. An economist wonders whether the mean income of female graduates from the local high school who work full-time but only have a high school is less than the national average. A random sample of 42 female graduates from this local high school who work full-time and only have their high school diploma found a mean income of $30,052. Assume that the population standard deviation for these incomes is $5,522, and that the level of significance for this hypothesis test is 5%. Use this information to answer the following questions:

a. Write out, using symbols, the null (HO) and alternative (HA) hypotheses.

b. Calculate the test statistic for this test.

c. Calculate the p-value for this test.

d. Is the null hypothesis rejected? Why or why not? Is this data statistically significant at the α = 0.02 level? (3 points)

Answer 1

a)

H0: = 31666

Ha: < 31666

b)

Test statistics

z = ( - ) / ( / sqrt(n) )

= (30052 - 31666) / (5522 / sqrt(42) )

= -1.89

c)

p-value = P(Z < z)

= P(Z < -1.89)

= 0.0294

d)

Since p-value > 0.02 significance level, do not reject H0.

We conclude that the data is not significant at = 0.02 significance level.