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Let us illustrate the idea of a sampling distribution in the case of a very small sample from a very small population. The population is the scores of 10 students on an exam:
Student 0 1 2 3 4 5 6 7 8 9Score 82 62 80 58 72 73 65 66 74 62
a. Use RAND function or StatTools to select 4 students randomly from the file below. What is the mean of the sample scores? This statistic is an estimate of the population mean.
b. Repeat this process 10 times or you can draw 10 samples simultaneously using StatTools. Make a histogram of the 10 values of sample means. You are constructing the sampling distribution of sample means. What is the center of your histogram?
c. Is the center of your histogram close to the population mean?
Assume that preparation D was a placebo. Use the Scheffe's procedure to compare the average response of A, B, C, and E to the response for D.
Is there evidence that the change was successful in reducing the wait time? (use 0.05 level of significance)
Use a 1% level of significance to test the claim that there are more calls during the night than in the day.
If statistically significant, do you think the difference is large enough to be important?
The following is the number of minutes to commute from home to work for a group of automobile executives.
Determine the probability that: a) Exactly 3 will have this mild side effect.
The level of satisfaction in a consumer survey would represent what level of measurement?
A sample of n= 16 scores has a mean of M = 45 and SS = 960. Calculate the sample standard deviation (s) and the estimated standard error for the sample means (SM).
During the past year, the mean sales of Wshington Reds in cases was 45,000 cases, and the standard deviaiton was 4,450. How many cases of Washington Reds should be brought to market? Assume the sales follow a normal distribution.
Discuss why sampling is essential to many research designs, and why, if done correctly may be more accurate than attempting census measurement.
Using the .10 level of significance, can we conclude that the assembly time using the new method is faster?
The lifetimes of light bulbs of a particular type are normally distributed with a mean of 370 hours and a standard deviation of 5 hours. What percentage of bulbs has lifetimes that lie within 1 standard deviation of the mean on either side?
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