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Masteriza [31]
3 years ago
14

The local swim team is considering offering a new semi-private class aimed at entry-level swimmers, but needs a minimum number o

f 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 _______.
Mathematics
1 answer:
SCORPION-xisa [38]3 years ago
7 0

Answer:

The significance level is \alpha=0.01 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:

z_{\alpha/2}= 2.326

So we reject the null hypothesis is z>2.326

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: \mu \leq 15

Alternative hypothesis: \mu > 15

And the statistic is given by:

z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

The significance level is \alpha=0.01 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:

z_{\alpha/2}= 2.326

So we reject the null hypothesis is z>2.326

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