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1. Health Care workers who use latex gloves with glove powder on a daily basis are particularly susceptible to developing a latex allergy. Each in a sample of 43 hospital employees who were diagnosed with a latex allergy based on a skin-prick test reported on their exposure to latex gloves. Summary statistics for the number of latex gloves used per week are x = 19.4 and s = 12.3. Complete parts (a) â€“ (d).
2. The white wood material used for the roof of an ancient temple is imported from a certain country. The wooden roof must withstand as much as 100 centimeters of snow in the winter. Architects at a university conducted a study to estimate the mean bending strength of the white wood roof. A sample of 25 pieces of the imported wood were tested and yielded the statistics x = 74.9 and s = 10.8 on breaking strength of the white wood with a 99% confidence interval. Interpret the result.
3. A group of researchers wants to estimate the true mean skidding distance along a new road in a certain forest. The skidding distances (in meters) were measured at 20 randomly selected road sites. These values are given in the accompanying table. Complete parts a through d.
4. In sociology, a personal network is defined as the people with whom you make frequent contact. A research program used a stratified random sample of men and women born between 1908 and 1937 to gauge the size of the personal network of older adults. Each adult in the sample was asked to â€œplease name the people you have frequent contact with and who are also important to you.â€? Based on the number of people named, the
personal network size for each adult was determined. The responses of 2,824 adults in this sample yielded statistics on network size, that is, the mean number of people named person was 14.3, with a standard deviation of 10.2. Complete parts a through c.
5. A newspaper reported that 50% of people say that some coffee shops are overpriced. The source of this information was a telephone survey of 40 adults.
6. A random sample of 1040 satellite radio subscribers was asked, â€œDo you have a satellite radio receiver in your car?â€? The survey found that 312 subscribes did, in fact, have a satellite receiver in their car.
7. In 2006, a survey of 400 adults in a region found that 45% had access to a highspeed Internet connection at home.
8. A gigantic warehouse stores approximately 80 million empty aluminum beer and soda cans. Recently, a fire occurred at the warehouse. The smoke from the fire contaminated many of the cans with black spot, rendering them unusable. A statistician was hired by the insurance company to estimate p, the true proportion of cans in the warehouse that were contaminated by their fire. How many aluminum cans should be randomly sampled to estimate p to within 0.08 with 90% confidence?
9. According to an article the bottled water you are drinking may contain more bacteria and other potentially carcinogenic chemicals than are allowed by state and federal regulations. O the more than 1300 bottles studied, nearly one-third exceeded government levels. Suppose that a department wants an updated estimate of the population proportion of bottled water that violates at least one government standard. Determine the sample size (number of bottles) needed to estimate this proportion to within +/- 0.02 with 99% confidence.
A company tests all new brands of golf balls to ensure that they meet certain specifications. One test conducted is intended to measure the average distance traveled when the ball is hit by a machine. Suppose the company wishes to estimate the mean distance for a new brand within 1.2 yards with 90% confidence. Assume that past tests have indicated that the standard deviation of the distances the machine hits golf balls is approximately 10 yards. How many golf balls should be hit by the machine to achieve the desired accuracy in estimating the mean?