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 10 randomly selected patients who went to the emergency room at rural hospitals waited an average of 6.9 hours to be admitted into the hospital. The standard deviation for these 10 patients was 1.3 hours. What can be concluded at the the a = 0.05 level of significance level of significance? a. For this study, we should use t-test for a population mean b. The null and alternative hypotheses would be: Họ: ?♥||Select an answer♥ Hj: ?v|| Select an answer♥ c. The test statistic ?v = (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.)

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Please answer B, C, & D. 

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 10 randomly selected patients who went to the emergency room at rural hospitals waited an average of 6.9 hours to be admitted. The standard deviation for these 10 patients was 1.3 hours. What can be concluded at the α = 0.05 level of significance?

a. For this study, we should use a **t-test for a population mean**.

b. The null and alternative hypotheses would be:
   - \( H_0: \mu = 7 \)
   - \( H_1: \mu \neq 7 \)

c. The test statistic \( t \) = -0.243 (please show your answer to 3 decimal places).

d. The p-value = 0.8133 (Please show your answer to 4 decimal places).

e. The p-value is \( > \alpha \).

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

g. Thus, the final conclusion is that:
   - 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 \( \alpha = 0.05 \). 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.
Transcribed Image Text: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 10 randomly selected patients who went to the emergency room at rural hospitals waited an average of 6.9 hours to be admitted. The standard deviation for these 10 patients was 1.3 hours. What can be concluded at the α = 0.05 level of significance? a. For this study, we should use a **t-test for a population mean**. b. The null and alternative hypotheses would be: - \( H_0: \mu = 7 \) - \( H_1: \mu \neq 7 \) c. The test statistic \( t \) = -0.243 (please show your answer to 3 decimal places). d. The p-value = 0.8133 (Please show your answer to 4 decimal places). e. The p-value is \( > \alpha \). f. Based on this, we should **fail to reject** the null hypothesis. g. Thus, the final conclusion is that: - 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 \( \alpha = 0.05 \). 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.
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