Question

You wish to test the following claim ( H 1 ) at a significance level of α = 0.025 . H o : μ = 50.6 H 1 : μ > 50.6 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 10 with a mean of ¯ x = 54.6 and a standard deviation of s = 10.5 . What is the critical value for this test

Answer 1

Answer: 1.205

Explanation:

Given : Significance level :
`\alpha=0.025`

`H_0:\mu=50.6\\\\H_1:\mu>50.6`

We assume that population is normally distributed.

The sample size :
`n=10`, which is less than 30 , so we apply t-test.

Mean :
`\overline{x}=54.6`

Standard deviation :
`\sigma=10.5`

The test statistic for population mean is given by :-

`t=\frac{\overline{x}-\mu_0}{(\sigma)/(√(n))}\\\\=(54.6-50.6)/((10.5)/(√(10)))=1.20467720387\approx1.205`

Hence, the critical value = 1.205