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Chapter 6: 60E (page 363)
If you wish to estimate a population mean with a sampling error of SE = .3 using a 95% confidence interval, and you know from prior sampling that is approximately equal to 7.2, how many observations would have to be included in your sample?
Sample of size n=18 observations Is required.
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Improving the productivity of chickens. Farmers have discovered that the more domestic chickens peck at objects placed in their environment, the healthier and more productive the chickens seem to be. White string has been found to be a particularly attractive pecking stimulus. In one experiment, 72 chickens were exposed to a string stimulus. Instead of white string, blue-colored string was used. The number of pecks each chicken took at the blue string over a specified time interval was recorded. Summary statistics for the 72 chickens were x = 1.13 pecks, s = 2.21 pecks (Applied Animal Behavior Science, October 2000).
a. Estimate population mean number of pecks made by chickens pecking at blue string using a 99% confidence interval. Interpret the result.
b. Previous research has shown that = 7.5 pecks if chickens are exposed to white string. Based on the results, part a, is there evidence that chickens are more apt to peck at white string than blue string? Explain.
Question: Heart rate variability of police officers. Are police officers susceptible to higher-than-normal heart rates? The heart rate variability (HRV) of police officers was the subject of research published in the American Journal of Human Biology (January 2014). HRV is defined as the variation in time intervals between heartbeats. A measure of HRV was obtained for each in a sample of 355 Buffalo, N.Y., police officers. (The lower the measure of HRV, the more susceptible the officer is to cardiovascular disease.) For the 73 officers diagnosed with hypertension, a 95% confidence interval for the mean HRV was (4.1, 124.5). For the 282 officers who are not hypertensive, a 95% confidence interval for the mean HRV was (148.0, 192.6).
a. What confidence coefficient was used to generate the confidence intervals?
b. Give a practical interpretation of both 95% confidence intervals. Use the phrase 鈥�95% confident鈥� in your answer.
c. When you say you are 鈥�95% confident,鈥� what do you mean?
d. If you want to reduce the width of each confidence interval, should you use a smaller or larger confidence coefficient? Explain.
Study of aircraft bird strikes. Refer to the InternationalJournal for Traffic and Transport Engineering(Vol. 3,2013) study of aircraft bird strikes at a Nigerian airport,Exercise 6.54 (p. 357). Recall that an air traffic controller
wants to estimate the true proportion of aircraft bird strikesthat occur above 100 feet. Determine how many aircraftbird strikes need to be analyzed to estimate the true proportionto within .05 if you use a 95% confidence interval.
Tipping points in daily deal transactions? Online 鈥渄aily deal鈥� sites (e.g., Groupon) offer customers a voucher to purchase a product at discount prices. However, the number of voucher purchases must exceed a predetermined number before the deal becomes active. This key number is termed the 鈥渢ipping point鈥� in marketing. Characteristics of the tipping point were investigated in the Journal of Interactive Marketing (February 2016). A sample of 2,617 vouchers purchased from daily-deal sites in Korea had a mean tipping point of 112 sales with a standard deviation of 560 sales. The researchers want to estimate the true mean tipping point of all daily deal offerings in Korea with 95% confidence. Find and practically interpret this interval estimate.
Eye shadow, mascara, and nickel allergies. Pigmented makeup products like mascara and eye shadow may contain metal (e.g., nickel) allergens. Is a nickel allergy more likely to occur in women who report cosmetic dermatitis from using eye shadow or mascara? This was the question of interest in a paper published in the Journal of the European Academy of Dermatology and Venereology (June 2010). In a sample of 131 women with cosmetic dermatitis from using eye shadow, 12 were diagnosed with a nickel allergy. In a sample of 250 women with cosmetic dermatitis from using mascara, 25 were diagnosed with a nickel allergy.
a. Compute a 95% confidence interval for the proportion of women with cosmetic dermatitis from using eye shadow who have a nickel allergy. Interpret the result.
b. Compute a 95% confidence interval for the proportion of women with cosmetic dermatitis from using mascara who have a nickel allergy. Interpret the result.
c. Suppose you are informed that the true proportion with a nickel allergy for one of the two groups (eye shadow or mascara) is .12. Can you determine which group is referenced? Explain.
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