Question

A hospital was concerned about reducing its wait time. A targeted wait time goal of 25 minutes was set. After implementing an improvement framework and? process, a sample of 364 patients showed the mean wait time was 23.06 ?minutes, with a standard deviation of 16.4 minutes. Complete parts? (a) and? (b) below. a. If you test the null hypothesis at the 0.10 level of? significance, is there evidence that the population mean wait time is less than 25 ?minutes? State the null and alternative hypotheses. A. Upper H 0?: mu greater than 25 Upper H 1?: mu less than 25 B. Upper H 0?: mu not equals 25 Upper H 1?: mu greater than or equals 25 C. Upper H 0?: mu greater than or equals 25 Upper H 1?: mu less than 25 D. Upper H 0?: mu greater than or equals 25 Upper H 1?: mu not equals 25 E. Upper H 0?: mu less than 25 Upper H 1?: mu greater than 25 F. Upper H 0?: mu less than 25 Upper H 1?: mu greater than or equals 25 Find the test statistic for this hypothesis test. t Subscript STATequals nothing ?(Type an integer or a decimal. Round to two decimal places as? needed.) Find the? p-value. The? p-value is nothing. ?(Type an integer or a decimal. Round to three decimal places as? needed.) Is there sufficient evidence to reject the null? hypothesis? (Use a 0.10 level of? significance.) A. Do not reject the null hypothesis. There is insufficient evidence at the 0.10 level of significance that the population mean wait time is less than 25 minutes. B. Reject the null hypothesis. There is sufficient evidence at the 0.10 level of significance that the population mean wait time is less than 25 minutes. C. Reject the null hypothesis. There is sufficient evidence at the 0.10 level of significance that the population mean wait time is greater than 25 minutes. D. Do not reject the null hypothesis. There is insufficient evidence at the 0.10 level of significance that the population mean wait time is greater than 25 minutes. b. Interpret the meaning of the? p-value in this problem. Choose the correct answer below. A. The? p-value is the probability that the actual mean wait time is 25 minutes given the sample mean wait time is 23.06 minutes. B. The? p-value is the probability of getting a sample mean wait time of 23.06 minutes or less if the actual mean wait time is 25 minutes. C. The? p-value is the probability that the actual mean wait time is more than 23.06 minutes. D. The? p-value is the probability that the actual mean wait time is 23.06 minutes or less.

Answer #1

The statistical software output for this problem is:

**One sample T summary hypothesis test:**

? : Mean of population

H_{0} : ? = 25

H_{A} : ? < 25

**Hypothesis test results:**

Mean |
Sample Mean |
Std. Err. |
DF |
T-Stat |
P-value |
---|---|---|---|---|---|

? | 23.06 | 0.85959357 | 363 | -2.2568805 | 0.0123 |

Hence,

a) Hypotheses:

Ho: ? = 25

Ha: ? < 25

t_{STAT} = -2.26

p - Value = 0.012

Reject the null hypothesis. There is sufficient evidence at the
0.10 level of significance that the population mean wait time is
less than 25 minutes. **Option B** is correct.

The? p-value is the probability of getting a sample mean wait
time of 23.06 minutes or less if the actual mean wait time is 25
minutes. **Option B** is correct.

A simple random sample of size nequals15 is drawn from a
population that is normally distributed. The sample mean is found
to be x overbarequals19.6 and the sample standard deviation is
found to be sequals6.3. Determine if the population mean is
different from 26 at the alpha equals 0.01 level of significance.
Complete parts (a) through (d) below. (a) Determine the null and
alternative hypotheses. Upper H 0: ▼ sigma mu p ▼ equals greater
than not equals less than...

A simple random sample of size nequals15 is drawn from a
population that is normally distributed. The sample mean is found
to be x overbarequals21.8 and the sample standard deviation is
found to be sequals6.3. Determine if the population mean is
different from 24 at the alpha equals 0.01 level of significance.
Complete parts (a) through (d) below. (a) Determine the null and
alternative hypotheses. Upper H 0: ▼ mu sigma p ▼ less than equals
greater than not equals...

A simple random sample of size nequals40 is drawn from a
population. The sample mean is found to be 104.3, and the sample
standard deviation is found to be 23.5. Is the population mean
greater than 100 at the alphaequals0.05 level of significance?
Determine the null and alternative hypotheses. Upper H 0: ▼ mu
less than 100 mu equals 100 mu greater than 100 mu less than 104.3
mu equals 104.3 mu greater than 104.3 Upper H 1: ▼ mu...

The lengths of time? (in years) it took a random sample of
3232
former smokers to quit smoking permanently are listed. Assume
the population standard deviation is
4.24.2
years. At
alpha?equals=0.060.06?,
is there enough evidence to reject the claim that the mean time
it takes smokers to quit smoking permanently is
1414
?years? Complete parts? (a) through? (e).
21.621.6
21.721.7
20.720.7
7.47.4
21.121.1
14.214.2
12.812.8
15.215.2
10.410.4
16.216.2
15.515.5
20.320.3
16.216.2
17.517.5
19.419.4
13.513.5
20.320.3
20.820.8
10.110.1
15.215.2
10.310.3
22.222.2...

A local chess club claims that the length of time to play a game
has a meanmean of less than 35 minutesless than 35 minutes. Write
sentences describing type I and type II errors for a hypothesis
test of this claim. A type I error will occur if the actual
meanmean of the length of time to play a game is less than or equal
to 3535 minutes, but you reject the null hypothesis, Upper H 0 :
mu less...

A psychologist obtains a random sample of 20 mothers in the
first trimester of their pregnancy. The mothers are asked to play
Mozart in the house at least 30 minutes each day until they give
birth. After 5 years, the child is administered an IQ test. It is
known that IQs are normally distributed with a mean of 100. If the
IQs of the 20 children in the study result in a sample mean of
104.4 and sample standard deviation...

A genetic experiment involving peas yielded one sample
of offspring consisting of 416 green peas and 165 yellow peas. Use
a 0.01 significance level to test the claim that under the same
circumstances, 27% of offspring peas will be yellow. Identify the
null hypothesis, alternative hypothesis, test statistic,
P-value, conclusion about the null hypothesis, and final
conclusion that addresses the original claim. Use the P-value
method and the normal distribution as an approximation to the
binomial distribution.
What are the...

A genetic experiment involving peas yielded one sample of
offspring consisting of 438 green peas and 161 yellow peas. Use a
0.01 significance level to test the claim that under the same
circumstances, 24% of offspring peas will be yellow. Identify the
null hypothesis, alternative hypothesis, test statistic,
P-value, conclusion about the null hypothesis, and final
conclusion that addresses the original claim. Use the P-value
method and the normal distribution as an approximation to the
binomial distribution.
A. Upper H...

8
The average wait time to get seated at a popular restaurant in
the city on a Friday night is 10 minutes. Is the mean wait time
greater for men who wear a tie? Wait times for 12 randomly selected
men who were wearing a tie are shown below. Assume that the
distribution of the population is normal.
8, 8, 9, 10, 9, 9, 8, 9, 12, 11, 12, 11
What can be concluded at the the αα = 0.10...

A genetic experiment involving peas yielded one sample of
offspring consisting of 411 green peas and 140 yellow peas. Use a
0.01 significance level to test the claim that under the same
circumstances, 27% of offspring peas will be yellow. Identify the
null hypothesis, alternative hypothesis, test statistic,
P-value, conclusion about the null hypothesis, and final
conclusion that addresses the original claim. Use the P-value
method and the normal distribution as an approximation to the
binomial distribution.
What are the...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 8 minutes ago

asked 36 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago