Chapter 8: Q82E (page 501)
a.Consider testing \(H0\) : \(\mu \)=80. Under what conditions should you use the t-distribution to conduct the test?
a.Two conditions to conduct the test for t-distribution
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The โwinnerโs curseโ in transaction bidding. In transaction bidding, the โwinnerโs curseโ is the miracle of the winning (or loftiest) shot price being above the anticipated value of the item being auctioned. The Review of Economics and Statistics (Aug. 2001) published a study on whether shot experience impacts the liability of the winnerโs curse being. Two groups of a stab in a sealed-shot transaction were compared (1)super-experienced stab and (2) less educated stab. In the super-experienced group, 29 of 189 winning flings were above the itemโs anticipated value; 32 of 149 winning flings were above the itemโs anticipated value in the less-educated group.
Drug content assessment. Scientists at GlaxoSmithKlineMedicines Research Center used high-performance liquidchromatography (HPLC) to determine the amountof drug in a tablet produced by the company (Analytical
Chemistry, Dec. 15, 2009). Drug concentrations (measuredas a percentage) for 50 randomly selected tablets are listedin the table below and saved in the accompanying file.
a. Descriptive statistics for the drug concentrations areshown at the top of the XLSTAT printout on the nextpage. Use this information to assess whether the dataare approximately normal.
b. An XLSTAT normal probability plot follows. Use thisinformation to assess whether the data are approximatelynormal.
91.28 92.83 89.35 91.90 82.85 94.83 89.83 89.00 84.62
86.96 88.32 91.17 83.86 89.74 92.24 92.59 84.21 89.36
90.96 92.85 89.39 89.82 89.91 92.16 88.67 89.35 86.51
89.04 91.82 93.02 88.32 88.76 89.26 90.36 87.16 91.74
86.12 92.10 83.33 87.61 88.20 92.78 86.35 93.84 91.20
93.44 86.77 83.77 93.19 81.79
Descriptive statistics(Quantitative data) | |
Statistic | Content |
Nbr.of Observation | 50 |
Minimum | 81.79 |
Maximum | 94.83 |
1st Quartile | 87.2725 |
Median | 89.375 |
3rd Quartile | 91.88 |
Mean | 89.2906 |
Variance(n-1) | 10.1343 |
Standard deviation(n-1) | 3.1834 |
Last name and acquisition timing. Refer to the Journal of Consumer Research (August 2011) study of the last name effect in acquisition timing, Exercise 8.13 (p. 466). Recall that the mean response times (in minutes) to acquire free tickets were compared for two groups of MBA studentsโ those students with last names beginning with one of the first nine letters of the alphabet and those with last names beginning with one of the last nine letters of the alphabet. How many MBA students from each group would need to be selected to estimate the difference in mean times to within 2 minutes of its true value with 95% confidence? (Assume equal sample sizes were selected for each group and that the response time standard deviation for both groups is โ 9 minutes.)
Producer willingness to supply biomass. The conversion of biomass to energy is critical for producing transportation fuels. How willing are producers to supply biomass products such as cereal straw, corn stover, and surplus hay? Economists surveyed producers in both mid-Missouri and southern Illinois (Biomass and Energy, Vol. 36, 2012). Independent samples of 431 Missouri producers and 508 Illinois producers participated in the survey. Each producer was asked to give the maximum proportion of hay produced that they would be willing to sell to the biomass market. Summary statistics for the two groups of producers are listed in the table. Does the mean amount of surplus that hay producers are willing to sell to the biomass market differ for the two areas, Missouri and Illinois? Use a = .05 to make the comparison.
Question: The purpose of this exercise is to compare the variability of with the variability of .
a. Suppose the first sample is selected from a population with mean and variance . Within what range should the sample mean vary about of the time in repeated samples of measurements from this distribution? That is, construct an interval extending standard deviations of on each side of .
b. Suppose the second sample is selected independently of the first from a second population with mean and variance . Within what range should the sample mean vary about the time in repeated samples of measurements from this distribution? That is, construct an interval extending standard deviations on each side .
c. Now consider the difference between the two sample means . What are the mean and standard deviation of the sampling distribution ?
d. Within what range should the difference in sample means vary about the time in repeated independent samples of measurements each from the two populations?
e. What, in general, can be said about the variability of the difference between independent sample means relative to the variability of the individual sample means?
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