Question

Consider the following hypothesis test: H 0: 50 H a: > 50 A sample of 50 is used and the population standard deviation is 6. Use the critical value approach to state your conclusion for each of the following sample results. Use = .05. a. With = 52.5, what is the value of the test statistic (to 2 decimals)? 2.42 Can it be concluded that the population mean is greater than 50? Yes b. With = 51, what is the value of the test statistic (to 2 decimals)? .97 Can it be concluded that the population mean is greater than 50? No c. With = 51.8, what is the value of the test statistic (to 2 decimals)? 1.65 Can it be concluded that the population mean is greater than 50? Yes

Answer 1

Explanation:

From the question we are told that:

Null Hypothesis
`H_0: 50`

Alternative Hypothesis
`H_a: > 50`

Sample size
`n=50`

standard deviation
`\sigma=6`

Significance level
`\alpha=0.05`

a)

Sample mean
`\=x=52.5`

Generally the equation for Test statistics is mathematically given by

`t=(\=x-\mu)/((\sigma)/(√(n) ) )`

`t=(52.5-50)/((6)/(√(50) ) )`

`t=2.95`

Therefore from table

`Critical\ value=1.645`

We conclude The value of test statistics is greater than critical value.

Therefore we Reject the Null hypothesis
`H_0`

b)

Sample mean
`\=x=51`

Generally the equation for Test statistics is mathematically given by

`t=(\=x-\mu)/((\sigma)/(√(n) ) )`

`t=(51-50)/((6)/(√(50) ) )`

`t=1.18`

Therefore from table

`Critical\ value=1.645`

We conclude,The value of test statistics is less than critical value.

Therefore we Fail to Reject the Null hypothesis
`H_0`

c)

Sample mean
`\=x=51`

Generally the equation for Test statistics is mathematically given by

`t=(\=x-\mu)/((\sigma)/(√(n) ) )`

`t=(51.8-50)/((6)/(√(50) ) )`

`t=2.12`

Therefore from table

`Critical\ value=1.645`

We conclude The value of test statistics is greater than critical value.

Therefore we Fail to Reject the Null hypothesis
`H_0`