1. Refer to the Real Estate data, which report information on the homes sold in Goodyear, Arizona, last year.
a. A recent article in the Arizona Republic indicated that the mean selling price of the homes in the area is more than $220,000. Can we conclude that the mean selling price in the Goodyear, AZ, area is more than $220,000? Use the .01 significance level. What is the p-value?
b. The same article reported the mean size was more than 2,100 square feet. Can we conclude that the mean size of homes sold in the Goodyear, AZ, area is more than 2,100 square feet? Use the .01 significance level. What is the p-value?
2. 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.
Click here for the Excel Data File
-0.38 -0.17 -0.26 -0.32 +0.35 -0.26 +0.37 +0.41 -0.09
-0.31 -0.42 -0.47 -0.46 -0.64 -0.09 -0.28 -0.59 +0.08
a-1. 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
3. 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 0.025 significance level is it reasonable to conclude the mean wedding cost is less than $10,000 as advertised?
12.4 8.5 10.1 12.6 10.5 9.1 9.8 11.2
a. State the null hypothesis and the alternate hypothesis. Use a .025 level of significance. (Enter your answers in thousands of dollars.)
H0: μ ≥
H1: μ <
b. State the decision rule for 0.025 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. What is the conclusion regarding the null hypothesis?
H0. The cost is than $10,000.
4. A cola-dispensing machine is set to dispense 9 ounces of cola per cup, with a standard deviation of 0.8 ounce. The manufacturer of the machine would like to set the control limit in such a way that, for samples of 37, 5% of the sample means will be greater than the upper control limit, and 5% of the sample means will be less than the lower control limit.
a. At what value should the control limit be set? (Round z values to two decimal places. Round your answers to 2 decimal places.)
Value should be in between and
b. If the population mean shifts to 8.6, what is the probability that the change will be detected? (Round your intermediate calculations to 2 decimal places and final answer to 4 decimal places.)
Probability
c. If the population mean shifts to 9.7, what is the probability that the change will be detected? (Round your intermediate calculations to 2 decimal places and final answer to 4 decimal places.)
Probability
5. A national grocer's magazine reports the typical shopper spends 8 minutes in line waiting to check out. A sample of 21 shoppers at the local Farmer Jack's showed a mean of 7.3 minutes with a standard deviation of 2.8 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 ≥ 8 and fail to reject H1: µ < 8 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 2 decimal places.)
c. What is your decision regarding H0?