Question

Asked Mar 11, 2019

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A hospital ER wants to determine if patients are waiting in the waiting room longer than 30 minutes. A random sample of 100 people was gathered. The mean waiting room time was 25 minutes with a standard deviation of 5.5 minutes. Is the value significantly greater than 15? Use a 5% level of significance. Give Ho and Ha. The appropriate test. Decision rule. Test calculations. Conclusion compared to alpha or critical value.

Step 1

**Test whether the population mean waiting time in the waiting room is statistically greater than 15 or not:**

Denote the population mean as μ*.*

Given that, the population mean waiting time in the waiting room is μ = 15 minutes, the population standard deviation is not known. Therefore, the *t-*distribution is used instead of standard normal distribution.

*The hypotheses are given below:*

*Null hypothesis:*

*H*_{0} : μ = 15

That is, the population mean waiting time in the waiting room is equal to 15.

*Alternative hypothesis:*

*H*_{1} : μ > 15 (Right tail test).

That is, the population mean waiting time in the waiting room is statistically greater than 15.

Step 2

**Obtain the test statistic value.**

The sample mean waiting time in the waiting room is *x*-bar = 25 minutes. The sample size is *n *= 100, the sample standard deviation in waiting time in the waiting room is *s *= 5.5 minutes.

The test statistic value is obtained as **18.1818 **from the calculation given below:

Step 3

**Obtain the critical value:**

The level of significance is α = 0.05.

From the *t *– distribution area va...

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