Question

Hugo, a pitcher, estimates that his pitch speed is more than 48 miles per hour, on average. Several of his teammates would like his estimate to be tested, so he decides to do a hypothesis test, at a 5% significance level, to persuade them. He throws 15 pitches, collects the proper data, and works through the testing procedure: H0: μ=48; Ha: μ>48 x¯=54 σ=5 α=0.05 (significance level) The test statistic is

Answer 1

The statistic would be given by:

`z=(\bar X-\mu_o)/((\sigma)/(√(n)))` (1)

Replacing the info given we got:

`z=(54-48)/((5)/(√(15)))=4.648`

Explanation:

Information given

`\bar X=54` represent the sample mean

`\sigma=5` represent the population deviation

`n=15` sample size

`\mu_o =48` represent the value to verify

`\alpha=0.05` represent the significance level

z would represent the statistic

System of hypothesis

We want to conduct a test in order to check the following :

Null hypothesis:
`\mu =48`

Alternative hypothesis:
`\mu > 48`

The statistic would be given by:

`z=(\bar X-\mu_o)/((\sigma)/(√(n)))` (1)

Replacing the info given we got:

`z=(54-48)/((5)/(√(15)))=4.648`