A survey of 100 similar-sized hospitals revealed a mean daily census in the pediatrics service of 27 with a standard deviation of 6.5. Researchers test whether these data provide sufficient evidence to indicate the mean is greater than 25. Use α=.05. Give 1. the hypotheses, 2. appropriate test, 3. decision rule, 4. calculated test statistic, and 5. conclusion with a comparison to the critical value or alpha.

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ChiKesselman ChiKesselman · Answer 1 · 2019-12-10T08:42:14+01:00

Answer:

We conclude that the mean is greater than 25.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 25

Sample mean, [tex]\bar{x}[/tex] = 27

Sample size, n = 100

Alpha, α = 0.05

Sample standard deviation, s = 6.5

First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 25\\H_A: \mu> 25[/tex]

We use One-tailed(right) z test to perform this hypothesis.

Formula:

[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }[/tex]

Putting all the values, we have

[tex]z_{stat} = \displaystyle\frac{27 - 25}{\frac{6.5}{\sqrt{100}} } = 3.07[/tex]

Now, [tex]z_{critical} \text{ at 0.05 level of significance } = 1.645[/tex]

Since,

[tex]z_{stat} > z_{critical}[/tex]

We reject the null hypothesis and accept the alternate hypothesis.

Thus, the mean is greater than 25.