Business Statistics HW
1)
The mean income per person in the United States is $44,500, and the distribution of incomes follows a normal distribution. A random sample of 16 residents of Wilmington, Delaware, had a mean of $52,500 with a standard deviation of $9,500. At the 0.05 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average?
a. State the null hypothesis and the alternate hypothesis.
H0: μ ≤
H1: μ >
b. State the decision rule for 0.050 significance level. (Round your answer to 3 decimal places.)
Reject H0 if t >
c. Compute the value of the test statistic. (Round your answer to 3 decimal places.)
Value of the test statistic
2)
A United Nations report shows the mean family income for Mexican migrants to the United States is $26,500 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 24 Mexican family units reveals a mean to be $30,150 with a sample standard deviation of $10,560. 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
3)
The American Water Works Association reports that the per capita water use in a single-family home is 65 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-one owners responded, and the sample mean water use per day was 63 gallons with a standard deviation of 9.1 gallons per day.
At the 0.10 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 ≥ 65 when the test statistic is (greater or less than) _____.
b.
The value of the test statistic is . (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
4)
Given the following hypotheses:
H0: μ ≤ 8
H1: μ > 8
A random sample of 10 observations is selected from a normal population. The sample mean was 11 and the sample standard deviation 4.6. Using the 0.100 significance level:
a. State the decision rule. (Round your answer to 3 decimal places.)
Reject H0 if t >
b.
Compute the value of the test statistic. (Round your answer to 3 decimal places.)
Value of the test statistic
5)
At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $82 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $3.26. Over the first 44 days she was employed at the restaurant, the mean daily amount of her tips was $84.61. At the 0.02 significance level, can Ms. Brigden conclude that her daily tips average more than $82?
a. State the null hypothesis and the alternate hypothesis.
H0: μ >82 ; H1: μ = 82
H0: μ ≥ 82 ; H1: μ < 82
H0: μ = 82 ; H1: μ ≠ 82
H0: μ ≤ 82 ; H1: μ > 82
b. State the decision rule.
Reject H0 if z > 2.05
Reject H1 if z > 2.05
Reject H0 if z < 2.05
Reject H1 if z < 2.05
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?
Do not reject H0
Reject H0
e. What is the p-value? (Round your answer to 4 decimal places.)
6)
The amount of water consumed each day by a healthy adult follows a normal distribution with a mean of 1.30 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:
1.36 1.35 1.33 1.66 1.58 1.32 1.38 1.42 1.90 1.54
At the 0.050 significance level, can we conclude that water consumption has increased? Calculate and interpret the p-value.
Picture Click here for the Excel Data File
a. 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 0.050 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 0.050 level, can we conclude that water consumption has increased?
H0 and conclude that water consumption has .
e. Estimate the p-value.
p-value is
7)
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.
Picture Click here for the Excel Data File
–0.42
–0.17
–0.11
–0.28
+0.33
–0.25
+0.34
+0.25
–0.08
–0.32
–0.54
–0.44
–0.45
–0.64
–0.04
–0.26
–0.44
+0.09
a-1.
Is it reasonable to conclude that the mean gain or loss in time for the watches is 0? Use the .10 significance level. At a level of .10 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
8)
The cost of weddings in the United States has skyrocketed in recent years. As a result, many couples are opting to have their weddings in the Caribbean. A Caribbean vacation resort recently advertised in Bride Magazine that the cost of a Caribbean wedding was less than $10,000. Listed below is a total cost in $000 for a sample of 8 Caribbean weddings. At the 0.050 significance level is it reasonable to conclude the mean wedding cost is less than $10,000 as advertised?
8.6
8.5
12.4
10.5
9.5
8.6
9.4
9.4
a.
State the null hypothesis and the alternate hypothesis. Use a .05 level of significance. (Enter your answers in thousands of dollars.)
H0: μ ≥
H1: μ <
b.
State the decision rule for 0.050 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Reject H0 if t <
c.
Compute 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.
