Question

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 10 randomly selected patients who went to the emergency room at rural hospitals waited an average of 6.2 hours to be admitted into the hospital. The standard deviation for these 10 patients was 2.5 hours. What can be concluded at the the αα = 0.01 level of significance level of significance?

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

H0: (μ, p) (?,>,=,<,≠)   

H1:(μ,p) (?,>,=,≠,<)

3. The test statistic (t,z)-____ = (please show your answer to 3 decimal places.)
4. The p-value =______ (Please show your answer to 4 decimal places.)
5. The p-value is (≤,>) α
6. Based on this, we should ( answer, reject, accept, fail) to reject the null hypothesis.
7. Thus, the final conclusion is that ______

a)The data suggest the populaton mean is significantly lower than 7 at αα = 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.

b)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.

c)The data suggest the population mean is not significantly lower than 7 at αα = 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.

Answer 1

a)
t-test for a population mean,

n)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 7
Alternative Hypothesis, Ha: μ < 7

c)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (6.2 - 7)/(2.5/sqrt(10))
t = -1.012

d)

P-value Approach
P-value = 0.1690

e)

The p-value is > α

f)

Based on this, we should fail to reject the null hypothesis.

g)

c)The data suggest the population mean is not significantly lower than 7 at αα = 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.