Question

(S 10.3) Suppose a random sample of size 15 is taken from a normally distributed population, and the sample mean and variance are calculated to be x¯=5.22 and s2=6.5respectively. Use this information to test the null hypothesis H0:?=5versus the alternative hypothesis HA:?<5, at the 10% level of significance. What is the value of the test statistic, for testing the null hypothesis that the population mean is equal to 5?____________ Round your response to at least 3 decimal places.

Answer 1

Sample size = n = 15

Sample mean = = 5.22

Sample variance = = 6.5

Sample standard deviation is square root of variance.

Sample standard deviation = s = 2.54951

The null and alternative hypothesis is

H0: ? = 5 versus HA: ? < 5

Level of significance = 0.10

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

Degrees of freedom = n - 1 = 15 - 1 = 14

P-value = P(T > 0.33) = 0.6284

P-value > 0.10 we fail to reject null hypothesis.

Conclusion: The population mean is equal to 5.