Question

Use aâ t-test to test the claim about the population mean at the given level of significance using the given sample statistics. Assume the population is normally distributed.

Claim: μ>77; α=0.05
Sample statistics: xÌ =78.6,s=3.7,n=23

a. What are the null and alternative hypotheses?
b. What is the value of the standardized test statistic?
c. What is the P-value of the test statistic?

Answer 1

a) NULL Hypothesis

`H_0:\mu \leq 77`

ALTERNATIVE hypotheses

`H_0: \mu>77`

b) Therefore t Critical value from table X is

`X=\pm 1.717`

c) Hence,we reject the Null hypothesis

Explanation:

From the question we are told that:

Claim:

`\mu=77`

Level of significance
`\alpha=0.05`

Sample mean
`\=x=78.6`

Sample Standard deviation
`\sigma=3.6`

Sample size
`n=23`

a)

Generally the equation for The null and alternative hypotheses is mathematically given by

NULL Hypothesis

`H_0:\mu \leq 77`

ALTERNATIVE hypotheses

`H_0: \mu>77`

b)

Generally the equation for The standardized test statistics t is mathematically given by

`t=((\=x-\mu))/((\sigma)/(√(n)))`

`t=((78.6-77))/((3.7)/(√(23)))`

`t=2.03`

Therefore Critical Value X is

`X=(\alpha,df)`

Where

`df=(23-1)\\\\df=22`

Therefore t Critical value from table X is

`X=\pm 1.717`

c)

The Test statistics is outside the Critical Value

Hence,we reject the Null hypothesis