Question 1 (2.85 points)
Eggs that are contaminated with salmonella can cause food poisoning among consumers. A large egg producer takes an SRS of 200 eggs from all the eggs shipped in one day. The laboratory reports that 11 of these eggs had salmonella contamination. Unknown to the producer, 0.2% (twotenths of one percent) of all eggs shipped had salmonella. In this situation,
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Suppose you interview 10 randomly selected workers and ask how many miles they commute to work. You’ll compute the sample mean commute distance. Now imagine repeating the survey many, many times, each time recording a different sample mean commute distance. In the long run, a histogram of these sample means represents
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The distribution of actual weights of 8 oz wedges of cheddar cheese produced at a dairy is Normal with mean 8.1 ounces and standard deviation 0.2 ounces.
Reference: Ref 115
The probability that the average amount charged over these 160 procedures is more than $1180 is
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In a large population of collegeeducated adults, the mean IQ is 112 with standard deviation 25. Suppose 300 adults from this population are randomly selected for a market research campaign.
Reference: Ref 114
The probability that the sample mean IQ is greater than 115 is
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In a large population of collegeeducated adults, the mean IQ is 112 with standard deviation 25. Suppose 300 adults from this population are randomly selected for a market research campaign.
Reference: Ref 114
The distribution of the sample mean IQ is
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The central limit theorem says that when a simple sample of size n is drawn from any population with mean μ and standard deviation σ, then when n is sufficiently large
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A survey of college students finds that 20% like country music, 15% like gospel music, and 10% like both country music and gospel music.
Reference: Ref 122
The proportion of students that like gospel music but not country music is
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A survey of college students finds that 20% like country music, 15% like gospel music, and 10% like both country music and gospel music.
Reference: Ref 122
The proportion of students that like neither country music nor gospel music is
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A survey of college students finds that 20% like country music, 15% like gospel music, and 10% like both country music and gospel music.
Reference: Ref 122
The proportion of students that like either country music or gospel music is
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A survey of college students finds that 20% like country music, 15% like gospel music, and 10% like both country music and gospel music.
Reference: Ref 122
The conditional probability that a student likes country music given that he or she likes gospel music is
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Suppose we toss a coin and roll a die. Let A be the event that the number of spots showing on the die is three or less and B be the event that the coin comes up heads. The events A and B are
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Spelling mistakes in a text are either nonword errors or word errors. A nonword error produces a string of letters that is not a word, such as “the” typed as “teh.” Word errors produce the wrong word, such as “loose” typed as “lose.” Nonword errors make up 25% of all errors. A human proofreader will catch 80% of nonword errors and 50% of word errors.
Reference: Ref 124
What percent of errors will the proofreader catch?
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A level 0.95 confidence interval is
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A medical researcher treats 400 subjects with high cholesterol with a new drug. The average decrease in cholesterol level is = 90 after two months of taking the drug. Assume that the decrease in cholesterol after two months of taking the drug follows a Normal distribution, with unknown mean μ and standard deviation σ = 30.
Reference: Ref 141
Which of the following would produce a confidence interval with a smaller margin of error than the 95% confidence interval you computed above?
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The time (in number of days) until maturity of a certain variety of tomato plant is Normally distributed with mean μ and standard deviation σ = 2.4. I select a simple random sample of four plants of this variety and measure the time until maturity. The sample yields = 65.
A 95% confidence interval for μ, in days, is
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The records of the 100 postal employees at a postal station in a large city showed that the average time these employees had worked for the postal service was = 9 years. Assume that we know that the standard deviation of the population of times U.S. Postal Service employees have spent with the postal service is approximately Normal, with standard deviation σ = 5 years. A 95% confidence interval for the mean time μ the population of U.S. Postal Service employees have spent with the postal service is
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The upper 0.05 critical value of the standard Normal distribution is
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I collect a random sample of size n from a population and from the data collected compute a 95% confidence interval for the mean of the population. Which of the following would produce a new confidence interval with smaller width (smaller margin of error) based on these same data?
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In formulating hypotheses for a statistical test of significance, the null hypothesis is often
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In their advertisements, the manufacturers of a certain brand of breakfast cereal would like to claim that eating their oatmeal for breakfast daily will produce a mean decrease in cholesterol of more than 10 points in one month for people with cholesterol levels over 200. In order to determine if this is a valid claim, they hire an independent testing agency, which then selects 25 people with a cholesterol level over 200 to eat their cereal for breakfast daily for a month. The agency should be testing the null hypothesis H_{0}: μ = 10 and the alternative hypothesis
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In a test of statistical hypotheses, the Pvalue tells us
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The scores of a certain population on the Wechsler Intelligence Scale for Children (WISC) are thought to be Normally distributed, with mean μ and standard deviation σ = 10. I wish to test whether the mean for this population differs from the national average of 100, so I use the hypotheses H_{0}: μ = 100 and H_{a}: μ ? 100, based on an SRS of size 25 from the population. I calculate a 95% confidence interval for μ and find it to be 100.76 to 106.24. Which of the following is true?
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Suppose we are testing the null hypothesis H_{0}: μ = 20 and the alternative H_{a}: μ 20, for a normal population with σ = 5. A random sample of 25 observations are drawn from the population, and we find the sample mean of these observations is = 17.6. The Pvalue is closest to
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The mean area μ of the several thousand apartments in a new development by a certain builder is advertised to be 1100 square feet. A tenant group thinks this is inaccurate, and suspects that the actual average area is less than 1100 square feet. In order to investigate this suspicion, the group hires an engineer to measure a sample of apartments to verify its suspicion. The appropriate null and alternative hypotheses, H_{0} and H_{a}, for μ are
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In a statistical test of hypotheses, we say the data are statistically significant at level α if
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A researcher wishes to determine if the use of an herbal extract improves memory. Subjects will take the herbal extract regularly during a 10week period of time. After this course of treatment, each subject has his or her memory tested using a standard memory test. Suppose the scores on this test of memory for all potential subjects taking the herbal extract follow a Normal distribution with mean μ and standard deviation σ = 6. Suppose also, that in the general population of all people, scores on the memory test follow a Normal distribution, with mean 50 and standard deviation σ = 4. The researcher, therefore, decides to test the hypotheses
H_{0}: μ = 50, H_{a}: μ > 50
To do so, the researcher has 100 subjects follow the protocol described above. The mean score for these students is = 55.2 and the Pvalue is less than 0.0001.
Reference: Ref 161
Suppose that another researcher attempts to replicate the study described above. She uses a sample of 10 subjects and observes a sample mean memory score of 55.2, the same as the sample mean described in the first study. It is appropriate to conclude which of the following?
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A radio show conducts a phonein survey each morning. Listeners are asked to call in with a response to the question of the day. One morning in 2011, listeners were asked if they supported or opposed term limits for members of Congress. Remarkably, 88% of listeners that called in favored term limits. We may safely conclude that
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The decrease in cholesterol level after eating a certain brand of oatmeal for breakfast for one month in people with cholesterol levels over 200 is Normally distributed, with mean (in milligrams) μ and standard deviation σ = 3. The brand advertises that eating its oatmeal for breakfast daily for one month will produce a mean decrease in cholesterol of more than 10 points for people with cholesterol levels over 200, but you believe that the mean decrease in cholesterol is actually less than advertised. To explore this, you test the hypotheses
H_{0}: μ = 10, H_{a}: μ < 10
and you obtain a Pvalue of 0.052. Which of the following is true?
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You plan to construct a confidence interval for the mean μ of a Normal population with (known) standard deviation σ. Which of the following will reduce the size of the margin of error?
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The scores of a certain population on the Wechsler Intelligence Scale for Children (WISC) are thought to be Normally distributed with mean μ and standard deviation σ = 10. A simple random sample of 25 children from this population is taken and each is given the WISC. The mean of the 25 scores is = 104.32.
Reference: Ref 142
Suppose a histogram of the 25 WISC scores is the following.
Based on this histogram, we would conclude that
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You measure the lifetime of a random sample of 64 tires of a certain brand. The sample mean is = 50 months. Suppose that the lifetimes for tires of this brand follow a normal distribution, with unknown mean μ and standard deviation σ = 5 kg. A 99% confidence interval for μ is
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A university administrator obtains a sample of the academic records of past and present scholarship athletes at the university. The administrator reports that no significant difference was found in the mean grade point average (GPA) for male and female scholarship athletes (P = 0.287). This means that
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Suppose that two very large companies (A and B) each select random samples of their employees. Company A had 5000 employees. Company B has 15,000 employees. In both surveys, the company will record the number of sick days taken by each sampled employee.
Reference: Ref 112
If each company randomly selects 50 employees for the survey, which of the following is true about the sampling distributions of the sample means (the mean number of sick days)?
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The sampling distribution of a statistic is
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In testing hypotheses, if the consequences of failing to reject a null hypothesis that is actually false are very serious, we should
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