Question

Given the following hypotheses:

H₀: μ ≤ 13

H₁: μ > 13

A random sample of 10 observations is selected from a normal population. The sample mean was 14 and the sample standard deviation 4.2. Using the 0.05 significance level:

1. State the decision rule. (Round your answer to 3 decimal places.)

2. Compute the value of the test statistic. (Negative answers should be indicated by a minus sign. Round your answer to 3 decimal places.)

Answer 1

Solution :

Given that ,

= 13  

= 14

s = 4.2

n = 10

The null and alternative hypothesis is ,

H₀ :     13

H_a : > 13

This is the right tailed test .

= 0.05  

df = n - 1 = 10 - 1 = 9

t = t_0.05,9 = 1.833

Reject Ho if t > 1.833

Test statistic = t

= ( - ) / s / n

= ( 14 - 13) / 4.2 / 10

= 0.753

The value of the test statistic = 0.753