Question

Given the following hypotheses: H0: μ = 450 H1: μ ≠ 450 A random sample of 11 observations is selected from a normal population. The sample mean was 456 and the sample standard deviation 5. Using the 0.10 significance level:

1. State the decision rule. (Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.)\

Reject H0 when the test statistic is _______inside or outside____, and interval is _____, ______

2. Compute the value of the test statistic. (Round your answer to 3 decimal places.)

Answer 1

Solution :

= 450

=456

S =11

n = 5

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :    = 450

H_a :     450

Test statistic = t

= ( - ) / S / n

= (456 - 450) / 5 / 11

= 1.220

Test statistic = t = 1.220

P-value =0.2896

= 0.10

P-value ≥

0.2896 ≥ 0.10

Fail to reject the null hypothesis .

There is not sufficient evidence to claim that the population mean μ is different than 450, at the 0.1 significance level.