Public health regulators try to maintain a level of fluoride in the public drinking water of 0.8 mg/L. In order to monitor this, they take samples from 9 randomly selected households drinking water each day to test the null hypothesis Ho : µ = 0. 8 vs Ha : µ # 0. 8. On this particular day, their measurements were: 0.81, 0.82,0.88, 0.82,0.81,0.90,0.81,0.80, and 0.82 Using this data, what is the p-value of this test? 0.0331 0.9835 0.0351 0.0165
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- A researcher conducted a study to investigate whether local car dealers tend to charge women more than men for the same car model. Using information from the county tax collector’s records, the researcher randomly selected one man and one woman from among everyone who had purchased the same model of an identically equipped car from the same dealer. The process was repeated for a total of 8 randomly selected car models. The purchase prices and the differences (woman – man) are shown in the table below. Summary statistics are also shown. Dotplots of the data and the differences are shown below. Do the data provide convincing evidence that, on average, women pay more than men in the county for the same car model?Cynthia, Mary, Mika, and Sallieof Hu’s Ur Dedi Cerveza Corp. conducted a survey on their 12-ounce cans to be sure that the variance of the amount of beer, in each can, was no more than 0.02square ounces. They collected a random sample of twenty cans of their 12-ounce beer, pulled from their production line, and got a sample variance of 0.015square ounces. Assume that the amount of beer in all 12-ounce cans to be normally distributed. Help them: a.Construct a 95% confidence interval for the population variance. b.Construct a 99% confidence interval for the standard deviation.A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in New York and Illinois. Due to recent trends in the childcare industry, the firm suspects that the that the mean annual income of childcare workers in the state of New York is greater than the mean annual income of childcare workers in Illinois. To see if this is true, the firm selected a random sample of 20 childcare workers from New York and an independent random sample of 20 childcare workers from Illinois and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars New York 46686 , 34979 , 47325 , 48892 , 51128 , 56792 , 47785 , 48995 , 57301 , 55176 , 48002 , 45718 , 50351 , 58527 , 47067 , 53699 , 54361 , 49727 , 36426 , 50870 Illinois 48009 , 46871 , 42774 , 49790 , 43163 , 45401 , 41068 , 50300 , 47064 , 42003 , 47775 , 41917…
- When 2 births are randomly selected, the sample space for genders is bb, bg, gb and gg. Assume that those 4 outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from 2 births. Dies the mean of the sample proportions equal the proportion of girls in 2 births? Does the result suggest that a sample proportion is an unbiased estimator of a population proportion? For the entire population, assume the probability of having a boy is 1/2, the probability of having s girl is 1/2 and this is not affected by how many boys or girls have previously been born. Determine the probabilities of each sample proportion, (type integers or simplified fractions)A business magazine mailed a questionnaire to the treasurers of all of the Top 400 most profitable companies, and received responses from 25% of them. Those responding reported that they did not find that such surveys intruded significantly on their workday. Identify any potential sources of bias you can detect and any problems you see in generalizing the population. Undercoverage is possible, since only treasurers of the top 400 profitable companies were surveyed instead of all treasurers. Nonresponse bias is possible, since treasurers who feel that surveys intrude on their workday would be less likely to respond. Convenience sampling bias is possible, since it is easier to get information from the treasurers at the top 400 profitable companies than at other companies. There is no indication of bias.Samples that are not chosen randomly from the population might exhibit bias True False
- Following an oil spill, a particular region of the ocean is being tested for the level of a chemical called naphthalene. It is considered fact that fish from the region will be safe to eat if, and only if, the mean naphthalene level in the region is less than 3.3 parts per billion. A set of water specimens will be randomly selected from the region and tested, and if the results provide convinving evidence that the mean naphthalene level is less than 3.3, then the sale of fish from the region will be made legal. Which of the following describes a Type I error and its consequences? A) the authorities fail to obtain convincing evidence that the mean naphthalene level is less than 3.3, and do not legalize the sale of fish from the region when in fact the fish are SAFE for consumption. B) The definition of a Type I error depends on the actual results of the study in question C) The authorities fail to obtain convincing evidence that the mean naphthalene level is less than 3.3, and do not…A lot of goods consisting of 2000 portable batteries will be controlled by the importing company. According to the acceptance sampling plan used, 2% of the lot is randomly selected, if at most 2.5% of the batteries in this sample are found to be defective, the party is accepted, otherwise it is rejected. a)Calculate the acceptance probabilities of the lot for the cases where the defective percentage is 0.5%, 1%, 2%, 3% and 8%.b)Plot the OC curve.c)If the producer risk is 1%, find and interpret the acceptable level of quality.d)If the consumer risk is 10%, find the level of refusable quality and interpret it.e)Show the acceptable quality level and the rejected quality level on the OC curve.A statistician selects a sample of 20 participants and makes the decision to retain the null hypothesis. He conducts the same study testing the same hypothesis with a sample of 100 participants and makes the decision to reject the null hypothesis. Provide a likely explanation for why the two samples led to different decisions.
- A warehouse manager wants to know if there is an association between the shift worked and being on time for work. To investigate, he selects a random sample of 70 workers and classifies each one according to the shift they worked most recently and whether they were on time for work. He was unable to classify a substantial number of people as being on time, so he classified those individuals as unknown. The data are displayed in the table. The manager would like to know if these data provide convincing evidence of an association between the shift worked and being on time in the large population of all workers at this warehouse. The random and 10% conditions are met. Is the Large Counts condition met? Yes, the smallest expected count is 5, so all expected counts are at least 5. Yes, the smallest expected count is 8.54, so all expected counts are at least 5. No, the smallest expected count is 2.56, so the expected counts are not all at least 5. No, the smallest expected count is…If a statistic used to estimate a parameter is such that the mean of its sampling distribution is equal to the true value of the parameter being estimated, then that statistic: 1. is a proportion. 2. is biased. 3. is unbiased. 4. has low variation. is random.When two births are randomly selected, the sample space for genders is BB, BG, GB, and GG. Assume that those four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from two births. Does the mean of the sample proportions equal proportion of girls in two births? Does the results suggest that a sample proportion is an unbiased estimator of a population proportion? For the entire population, assume the probability of having a boy is 1/2, the probability of having a girl as 1/2 and this is not affected by how many boys or girls have previously been born