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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 lower waiting time? The 13 randomly selected patients who went to the emergency room at rural hospitals waited an average of 6.3 hours to be admitted into the hospital. The standard deviation for these 13 patients was 1.3 hours. What can be concluded at the the
α
= 0.01 level of significance level of significance?

For this study, we should use
Select an answer
The null and alternative hypotheses would be:

H
0
:

?

Select an answer




H
1
:

?

Select an answer



The test statistic
?
=
(please show your answer to 3 decimal places.)
The p-value =
(Please show your answer to 4 decimal places.)
The p-value is
?

α

Based on this, we should
Select an answer
the null hypothesis.
Thus, the final conclusion is that ...
The data suggest the population mean is not significantly lower than 7 at
α
= 0.01, 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.
The data suggest the populaton mean is significantly lower than 7 at
α
= 0.01, 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 lower than 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 lower than 7 hours at
α
= 0.01, 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 lower than 7 hours.

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  1. For this study, we should use t-test and the null and alternative hypotheses would be given by H₀: μ = 7 and H₁: μ < 7.
  2. The test statistic is -1.941 and the p-value (0.0381) is greater than α = 0.01.
  3. Based on this, we should fail to reject the null hypothesis.
  4. Thus, the final conclusion is that the data suggest the population mean is not significantly lower than 7 at α = 0.01, 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.

What is a null hypothesis?

A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.

How to calculate value of the test statistic?

The test statistics can be calculated by using this formula:

[tex]t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]

Where:

  • x is the sample mean.
  • u is the mean.
  • is the standard deviation.
  • n is the number of hours.

For this study, we should use t-test and the null and alternative hypotheses would be given by:

H₀: μ = 7

H₁: μ < 7

[tex]t=\frac{6.3\;-\;7}{\frac{1.3}{\sqrt{13} } }\\\\t=\frac{-0.7}{\frac{1.3}{3.6056 } }[/tex]

t = -0.7/0.3606

t = -1.941.

For the p-value, we have:

P-value = P(t < -1.9412)

P-value = 0.0381.

Therefore, the p-value (0.0381) is greater than α = 0.01. Based on this, we should fail to reject the null hypothesis.

Thus, the final conclusion is that the data suggest the population mean is not significantly lower than 7 at α = 0.01, 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.

Read more on null hypothesis here: https://brainly.com/question/14913351

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