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.)

Please explain and give full answers

Answer 1

Given the following hypotheses:

H0: μ = 450

H1: μ ≠ 450

Under Ho: Our test statistics :

Critical region:

We have sufficient evidence to reject Ho at 10% level of significance.

We accept the claim that population mean  

Alternatively, we can find the p-value of this t-test:

We use the Student's t- distribution test to find the p-value:

p	0.005	0.001
df
10	3.169	4.144

The p-value is between 0.005 and 0.001

p-value = 0.002601

Since, p-value is less than we have sufficient evidence to reject Ho at 10% level of significance.