Question

Formal education (in years) was measured for a sample of low-income adults and a sample of high-income adults. A researcher hypothesizes that lower income adults have significantly less formal education than high income adults and sets an alpha of 0.05. Low-income adults (N = 38) have a mean of 12.5 years with a standard deviation of 3.4. High-income adults (N=47) had a mean of 14.3 and a standard deviation of 2.5.

a) Is this a one-sample test or a two-sample test?

b) Is this a one-tailed test or a two-tailed test?

c) Which test statistic will you calculate?

d) Please compute the test statistic to the second decimal:

e) What is the appropriate cut-off value?

f) Is the result statistically significant? Yes/no

Answer 1

Solution:

Given claim is,

Lower income adults have significantly less formal education than high income adults.

Suppose sample 1 :Lower income adults

sample 2 :high income adults.

a) This test is two sample test

b) This is one tailed test as alternative hypothesis contains less than.

from part c - f will appear in following 5 step hypothesis test

We are given,

= 12.5 , = 14.3

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean ?1? is less than ?2?, at the 0.05 significance level. Hence we can say that given claim is correct.

Done