Nationally, patients who go to the emergency room wait an average of 7 hours to be admitted into the hospital. Do patients at rural hospitals have a different waiting time? The 12 randomly selected patients who went to the emergency room at rural hospitals waited an average of 6.8 hours to be admitted into the hospital. The standard deviation for these 12 patients was 1.3 hours. What can be concluded at the the αα = 0.05 level of significance level of significance?For this study, we should use Select an answer t-test for a population mean z-test for a population proportion The null and alternative hypotheses would be:      H0:H0:  ? p μ  ? = ≠ > <        H1:H1:  ? μ p  ? > < = ≠    The test statistic ? z t  =  (please show your answer to 3 decimal places.)The p-value =  (Please show your answer to 4 decimal places.)The p-value is ? > ≤  ααBased on this, we should Select an answer accept fail to reject reject  the null hypothesis.Thus, the final conclusion is that ...The data suggest the populaton mean is significantly different from 7 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is different from 7 hours.The data suggest that the population mean awaiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is not significantly different from 7 hours at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is different from 7 hours.The data suggest the population mean is not significantly different from 7 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is equal to 7 hours.

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Asked Nov 18, 2019
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Nationally, patients who go to the emergency room wait an average of 7 hours to be admitted into the hospital. Do patients at rural hospitals have a different waiting time? The 12 randomly selected patients who went to the emergency room at rural hospitals waited an average of 6.8 hours to be admitted into the hospital. The standard deviation for these 12 patients was 1.3 hours. What can be concluded at the the αα = 0.05 level of significance level of significance?

  1. For this study, we should use Select an answer t-test for a population mean z-test for a population proportion 
  2. The null and alternative hypotheses would be:     

 H0:H0:  ? p μ  ? = ≠ > <       

 H1:H1:  ? μ p  ? > < = ≠    

  1. The test statistic ? z t  =  (please show your answer to 3 decimal places.)
  2. The p-value =  (Please show your answer to 4 decimal places.)
  3. The p-value is ? > ≤  αα
  4. Based on this, we should Select an answer accept fail to reject reject  the null hypothesis.
  5. Thus, the final conclusion is that ...
    • The data suggest the populaton mean is significantly different from 7 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is different from 7 hours.
    • The data suggest that the population mean awaiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is not significantly different from 7 hours at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is different from 7 hours.
    • The data suggest the population mean is not significantly different from 7 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is equal to 7 hours.
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Expert Answer

Step 1

1)The t-test statistic:

Here, the sample size is small and sample standard deviation is unknown. Therefore, t-test for population mean is appropriate in this case.

Step 2

(2) Hypotheses and calculation of test statistic:

The hypotheses to be tested are:

H0: μ = 7, that is, average waiting time is 7 hrs;

Versus:

H0: μ ≠ 7, that is, the average waiting time is not 7 hrs;

A sample of 12 patients is considered. It was found that the average waiting time was 6.8 hours with standard deviation 1.3 hours.

The test statistic is obtained as follows:

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t = n 6.8 7 1.3 V12 -0.533

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Step 3

p-value:

For sample size n, the degrees of freedom (df) is n – 1. Here, df = 12 – 1 = 11.

The p-value is found using Excel, by using t...

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