Question

This requires you to show ALL work needed to conduct the two tests of hypotheses below. Determine if your tests are one tailed or two-tailed according to your alternative hypothesis. You will have to use a z table as well.

1) A random sample of 20 observations selected from a normal population produced x bar = 72.6 and s^2 (variance) = 19.4

a) Test the null hypothesis: mean = 80 against the alternative hypothesis: mean < 80. Use alpha = .05

b) Test the null hypothesis: mean = 80 against the alternative hypothesis: mean "not equal" 80. Use alpha = .01

Answer 1

a)

here this is left tailed test as we are checking if mean is lower than what was assumed:

as test statistic is less than critical value we rejet null hypothesis

we have sufficient evidence to conclude that population mean is less than 80.

b)

this is two tailed test ; as we are nt checking if mean is higher or lower than assumed value

as test statistic is in critical region we rejet null hypothesis

we have sufficient evidence to conclude that population mean is different from 80.