Recall that ims that very large data digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data bank. You draw a random sample of n = 227 numbers from this file and r = 85 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1. (i) Test the claim that p is more than 0.301. Use α = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. OHO: P= 0.301; H₁: p > 0.301 OHO: p > 0.301; H₁: p = 0.301 OH: P = 0.301; H₂: p = 0.301 O Ho: P= 0.301; H₂: p < 0.301 (b) What sampling distribution will you use? O The standard normal, since np < 5 and nq < 5. The Student's t, since np < 5 and nq < 5. O The Student's t, since np > 5 and nq > 5. O The standard normal, since np > 5 and nq > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.)

A random sample of 300 physicians shows that there are 50 of them who make at least $200,000 a year. What is the test statistic if we want to test that the true proportion of physicians in the population who make at least $200,000 a year is less than 0.20?

An adventure company runs two obstacle courses, Fundash and Coolsprint. The designer of the courses suspects that the mean completion time of Fundash is not equal to the mean completion time of Coolsprint. To test this, she selects 250 Fundash runners and 285 Coolsprint runners. (Consider these as random samples of the Fundash and Coolspring runners.) The 250 Fundash runners complete the course with a mean time of 76.7 minutes and a standard deviation of 5.7 minutes. The 285 Coolsprint runners complete the course with a mean time of 77.5 minutes and a standard deviation of 5.6 minutes. Assume that the population standard deviations of the completion times can be estimated to be the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.05 level of significance, is there enough evidence to support the claim that the mean completion time, u, of Fundash is not equal to the mean completion time, µa, of Coolsprint? Perform a two-tailed test.…

Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 38 arrests last month, 21 were of males aged 15 to 34 years. Use a 1% level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%. LAUSE SALT (a) What is the level of significance? ← State the null and alternate hypotheses. OM P=0.7; M₁: P 5 and ng> 5. O The Student's t, since np> 5 and ng 5. O The Student's t, since np < 5 and ng < 5 O The standard normal, since np < 5 and ng < 5 What is the value of the sample test statistic? (Round your answer to two decimal places) - (C)…

Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 yearst. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 38 arrests last month, 24 were of males aged 15 to 34 years. Use a 10% level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: P = 0.7; H₁: p > 0.7 Ho: P = 0.7; H₁: P = 0.7 O Ho: P = 0.7; H₁: p 5 and nq > 5. O The Student's t, since np 5 and nq > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the P-value of the test statistic.…

News reports speak of an emerging crisis of childhood obesity in the United States. The National Health and Nutrition Examination Survey (NHANES) is a government survey run every several years recording a number of vital statistics on a random sample of Americans. A body mass index (BMI) is computed for each individual in the sample based on the individual's height and weight. Here are sample results for 8-year-old boys over the past 40 years. The table gives the sample size for 3 different surveys, the sample mean and sample standard deviation. Suppose we want to run an ANOVA to see if there is a difference in mean BMI for the three surveys. Assume each survey is a random sample and there are no extreme outliers.What is the sample standard deviations for each survey? ...the NHES II study?  ...the NHANES II study?  ...the NHANES study?

Does it seem to you that people tend to be absent more on some days of the week than on others? Recently, a major biotechnology firm collected data with the hope of determining whether or not its employees were more likely to be absent on some weekdays than on others. The firm examined a random sample of 130 employee absences. The distribution of these 130 absences is shown in the table below. The observed frequency for each category (each weekday) is shown in the first row of numbers. The second row of numbers contains the frequencies expected for a sample of 130 employees if employee absences at the firm are equally likely on each of the five weekdays. The bottom row of numbers contains the following value for each of the categories.

Suppose you know the percentage of foul shots a basketball player makes during the season. You want to estimate the expected number of shots made in 10 shots.  You simulate 10 shots 25 times and get the following numbers of shots made:   7  9  7  6  3  7  5  6  5  6  7  5  6  6  8  5  6  3  9  6  7  7  8  7  9

On average, a sample of n = 36 scores will provide a better estimate of the population mean than a sample of n = 49 scores from the same population.

Describe a study in which you can use both nonparametric and parametric statistics. A researcher has participants expecting to receive either painful or mild electrical shocks during a study wait in a quarter-full waiting room with other participants. He then measures whether they choose to sit next to other participants or if they sit far away on their own. What is the best test to run for this study and why?