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The local swim team is considering offering a new semi-private class aimed at entry-level swimmers, but needs a minimum number of swimmers to sign up in order to be cost effective. Last year’s data showed that during eight swim sessions the average number of entry-level swimmers attending was 15. Suppose the instructor wants to conduct a hypothesis test and the alternative hypothesis is "the population mean is greater than 15." If the sample size is five, σ is known, and α = .01, the critical value of z is _______.

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Answer:

The significance level is [tex]\alpha=0.01[/tex] and since we are conducting a right tailed test we need to find a critical value who accumulate 0.01 of the area in the right of the normal standard distribution and we got:

[tex] z_{\alpha/2}= 2.326[/tex]

So we reject the null hypothesis is [tex] z>2.326[/tex]

Step-by-step explanation:

For this case we define the random variable X as the number of entry-level swimmers and we are interested about the true population mean for this variable . On specific we want to test this:

Null hypothesis: [tex]\mu \leq 15[/tex]

Alternative hypothesis: [tex]\mu > 15[/tex]

And the statistic is given by:

[tex] z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

The significance level is [tex]\alpha=0.01[/tex] and since we are conducting a right tailed test we need to find a critical value who accumulate 0.01 of the area in the right of the normal standard distribution and we got:

[tex] z_{\alpha/2}= 2.326[/tex]

So we reject the null hypothesis is [tex] z>2.326[/tex]

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