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

Answer:

The statistic would be given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)    

Replacing the info given we got:

$z=\frac{54-48}{\frac{5}{\sqrt{15}}}=4.648$    

Step-by-step 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:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)    

Replacing the info given we got:

$z=\frac{54-48}{\frac{5}{\sqrt{15}}}=4.648$