At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $88 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $2.50. Over the first 50 days she was employed at the restaurant, the mean daily amount of her tips was $89.93. At the 0.10 significance level, can Ms. Brigden conclude that her daily tips average more than $88?
a.
State the null hypothesis and the alternate hypothesis.
H0: μ >88 ; H1: μ = 88
H0: μ ≥ 88 ; H1: μ < 88
H0: μ = 88 ; H1: μ ≠ 88
H0: μ ≤ 88 ; H1: μ > 88
b.
State the decision rule.
Reject H1 if z < 1.28
Reject H1 if z > 1.28
Reject H0 if z < 1.28
Reject H0 if z > 1.28
c.
Compute the value of the test statistic. (Round your answer to 2 decimal places.)
Value of the test statistic
d.
What is your decision regarding H0?
Reject H0
Do not reject H0
e.
What is the p-value? (Round your answer to 4 decimal places.)
p-value
2.A sample of 39 observations is selected from a normal population. The sample mean is 31, and the population standard deviation is 5. Conduct the following test of hypothesis using the 0.05 significance level.
H0 : μ ≤ 30
H1 : μ > 30
a.
Is this a one- or two-tailed test?
“Two-tailed”-the alternate hypothesis is different from direction.
“One-tailed”-the alternate hypothesis is greater than direction.
b.
What is the decision rule? (Round your answer to 3 decimal places.)
H0, when z >
c.
What is the value of the test statistic? (Round your answer to 2 decimal places.)
Value of the test statistic
d.
What is your decision regarding H0?
Do not reject
Reject
There is evidence to conclude that the population mean is greater than 30.
e.
What is the p-value? (Round your answer to 4 decimal places.)
p-value
3.
The following information is available.
H0 : μ ≥ 220
H1 : μ < 220
A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .025 significance level.
a.
Is this a one- or two-tailed test?
Two-tailed test
One-tailed test
b.
What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)
H0 when z <
c.
What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Value of the test statistic
d.
What is your decision regarding H0?
Reject
Do not reject
e.
What is the p-value? (Round your answer to 4 decimal places.)
p-value
The amount of water consumed each day by a healthy adult follows a normal distribution with a mean of 1.50 liters. A sample of 10 adults after the campaign shows the following consumption in liters. A health campaign promotes the consumption of at least 2.0 liters per day:
1.52 1.64 1.66 1.40 1.82 1.70 1.90 1.45 1.78 1.92
At the 0.010 significance level, can we conclude that water consumption has increased? Calculate and interpret the p-value.
State the null hypothesis and the alternate hypothesis. (Round your answers to 2 decimal places.)
H0: μ ≤
H1: μ >
b.
State the decision rule for 0.010 significance level. (Round your answer to 3 decimal places.)
Reject H0 if t >
c.
Compute the value of the test statistic. (Round your intermediate and final answer to 3 decimal places.)
Value of the test statistic
d.
At the 0.010 level, can we conclude that water consumption has increased?
H0 and conclude that water consumption has .
e.
Estimate the p-value.
p-value is
5.Watch Corporation of Switzerland claims that its watches on average will neither gain nor lose time during a week. A sample of 18 watches provided the following gains (+) or losses (–) in seconds per week.
Is it reasonable to conclude that the mean gain or loss in time for the watches is 0? Use the .05 significance level. At a level of .05 significance, we reject H0: μ = 0 if t < or t >. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
a-2.
The value of the test statistic is . (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
a-3.
H0: μ = 0. The p-value is
6.
A United Nations report shows the mean family income for Mexican migrants to the United States is $28,540 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 26 Mexican family units reveals a mean to be $30,500 with a sample standard deviation of $10,500. Does this information disagree with the United Nations report? Apply the 0.01 significance level.
a.
State the null hypothesis and the alternate hypothesis.
H0: μ =
H1: μ ≠
b.
State the decision rule for .01 significance level. (Negative amounts should be indicated by a minus sign.Round your answers to 3 decimal places.)
Reject H0 if t is not between and
c.
Compute the value of the test statistic. (Round your answer to 3 decimal places.)
Value of the test statistic
d.
Does this information disagree with the United Nations report? Apply the 0.01 significance level.
. This data the report.
7.
A national grocer’s magazine reports the typical shopper spends 5 minutes in line waiting to check out. A sample of 15 shoppers at the local Farmer Jack’s showed a mean of 4.2 minutes with a standard deviation of 3.8 minutes.
Is the waiting time at the local Farmer Jack’s less than that reported in the national magazine? Use the 0.010 significance level.
a.
What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Reject H0: µ ≥ 5 when the test statistic is .
b.
The value of the test statistic is . (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
c.
What is your decision regarding H0?
Do not reject H0
Reject H0
8.
The American Water Works Association reports that the per capita water use in a single-family home is 80 gallons per day. Legacy Ranch is a relatively new housing development. The builders installed more efficient water fixtures, such as low-flush toilets, and subsequently conducted a survey of the residences. Twenty-six owners responded, and the sample mean water use per day was 78 gallons with a standard deviation of 7.2 gallons per day.
At the 0.01 level of significance, is that enough evidence to conclude that residents of Legacy Ranch use less water on average?
a.
What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Reject H0: µ ≥ 80 when the test statistic is
.
b.
The value of the test statistic is
. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
c.
What is your decision regarding H0?
Reject
Fail to reject
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