Statistics: Tweens, Rainfall, Body Temperature
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Exercise 1
When it comes to advertising, "'tweens" are not ready for the hard line messages that advertisers often use to reach teenagers. The Geppeto Group study found that 78% of 'tweens understand and enjoy ads that are silly in nature. Suppose that the study involved n = 1030 'tweens.
a. Construct a 90% confidence interval for the proportion of 'tweens who understand and enjoy ads that are silly in nature.
b. Do you think that "more than 75%" of all 'tweens enjoy ads that are silly in nature? Why?
Exercise 2
What is the normal body temperature for healthy humans? A random sample of 130 healthy human body temperatures provided by Allen Shoemaker yielded x (with a line over it) =98.25 degrees and standard deviation 0.73 degrees.
a. Give a 99% confidence interval for the average body temperature of healthy people.
b.Does the confidence interval obtained in part (a) contain the value 98.6 degrees, the accepted average temperature cited by physicians and others? What conclusions can you draw?
Exercise 3
Refer to Exercise 1. How many 'tweens should have been interviewed in order to estimate the proportion of 'tweens who understand and enjoy ads that are silly in nature, correct to within .02, with probability .99? Use the proportion from the previous sample in approximating the standard error of the estimate.
Exercise 4
Suppose that you want to estimate the mean pH of rainfalls in an area that suffers from heavy pollution due to the discharge of smoke from a power plant. Assume that - is in the neighborhood of .5 pH and that you want your estimate to lie within .1 of ? with probability near .95. Approximately how many rainfalls must be included in your sample (one pH reading per rainfall)? Would it be valid to select all of your water specimens from a single rainfall? Explain.
Exercise 5
Although there are many treatments for bulimia nervosa, some subjects fail to benefit from treatment. In a study to determine which factors predict who will benefit from treatment, Wendy Baell and E. H. Wertheim found that self-esteem was one of the important predictors. The mean and standard deviation of post treatment self esteem scores for n = 21 subjects were x (with a line over)= 26.6 and s = 7.4, respectively. Find a 95% confidence interval for the true post treatment self esteem scores.
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Solution Summary
The expert examines a tweens, rainfall and body temperatures are examined.
Solution Preview
1.
a.
The critical value for 90% confidence interval is 1.645
Margin of error=critical value*standard error=1.645*sqrt(0.78*(1-0.78)/1030)=0.021
Upper limit: 0.78+0.021=0.801
Lower limit: 0.78-0.021=0.759
Therefore, the 90% confidence interval for the mean proportion is [0.759,0.801].
b.
since all values in the 90% confidence interval is larger than 0.75, we could conclude that "more than 75%" of all 'tweens enjoy ads that are ...
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