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.

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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.

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Expert Answer

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:

H0 : μ = 15

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

Alternative hypothesis:

H1 : 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:

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Step 3

Obtain the critical value:

The level of significance is α = 0.05.

From the t – distribution area va...

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Hypothesis Testing

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