Question

1. In order to test H0: µ=40 versus H1: µ > 40, a random sample of size n=25 is obtained from a population that is known to be normally distributed with sigma=6.

. The researcher decides to test this hypothesis at the α =0.1 level of significance, determine the critical value.

b. The sample mean is determined to be x-bar=42.3, compute the test statistic z=???

c. Draw a normal curve that depicts the critical region and declare if the null should be rejected or not rejected.

Answer 1

GIVEN:

Sample size

Population standard deviation

Sample mean

HYPOTHESIS:

(That is, the population mean is not significantly different from 40)

(That is, the population mean is significantly different from 40)

LEVEL OF SIGNIFICANCE:

(a) CRITICAL VALUE:

The right tailed z critical value at significance level   is .

(b) TEST STATISTIC:

  

  

(c) REJECTION/ CRITICAL REGION:

CONCLUSION:

Since the calculated z statistic (1.92) is greater than the critical value (1.28), we reject the null hypothesis and conclude that the population mean is significantly different from 40.