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Chapter 10: Q. 68 (page 659)

There are two common methods for measuring the concentration of a pollutant in fish tissue. Do the two methods differ on average? You apply both methods to a random sample of 18carp and use

(a) the paired t-test for μd.

(b) the one-sample z test for p.

(c) the two-sample t-test forμ1-μ2

(d) the two-sample z test for p1-p2

(e) none of these.

Short Answer

Expert verified

Apply both methods to a random sample of 18 carp and use option (a) the paired t-test for μd.

Step by step solution

01

Given information

The two common methods for measuring the concentration of a pollutant in fish tissue.

Random sample=18carp

02

Explanation

One proportion: one-sample z test/interval

Two proportion: two-sample z test/interval

One mean: one-sample t-test/interval

Mean difference: two-sample t-test/interval

Two means or mean differences with paired data in the two samples: paired t-test/interval

Use a test if you want to test for a difference, equality, increase or decrease. Use an interval if you want to estimate an interval in which the true value lies.

Paired t-test forμd.

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Most popular questions from this chapter

Which of the following is false?

(a) A measure of center alone does not completely describe the characteristics of a set of data. Some measure of spread is also needed.

(b) If the original measurements are expressed in inches, the standard deviation would be expressed in square inches.

(c) One of the disadvantages of a histogram is that it doesn’t show each data value.

(d) Between the range and the interquartile range, the IQR is a better measure of spread if there are outliers.

(e) If a distribution is skewed, the median and interquartile range should be reported rather than the mean and standard deviation.

Dropping out You have data from interviews with a random sample of students who failed to graduate from a particular college in 7years and also from a random sample of students who entered at the same time and did graduate. You will use these data to compare the percentages of students from rural backgrounds among dropouts and graduates.

Quality control (2.2,5.3,6.3)Many manufacturing companies use statistical techniques to ensure that the products they make meet standards. One common way to do this is to take a random sample of products at regular intervals throughout the production shift. Assuming that the process is working properly, the mean measurements from these random samples will vary Normally around the target mean μ, with a standard deviation of σ. For each question that follows, assume that the process is working properly.

(a) What's the probability that at least one of the next two sample means will fall more than 2σfrom the target mean μ? Show your work.

(b) What's the probability that the first sample mean that is greater than μ+2σis the one from the fourth sample taken?

(c) Plant managers are trying to develop a criterion for determining when the process is not working properly. One idea they have is to look at the 5 most recent sample means. If at least 4of the 5 fall outside the interval(μ-σ,μ+σ), they will conclude that the process isn't working. Is this a reasonable criterion? Justify your answer with an appropriate probability.

A study by the National Athletic Trainers Association surveyed random samples of 1679high school freshmen and 1366high school seniors in Illinois. Results showed that 34of the freshmen and 24 of the seniors had used anabolic steroids. Steroids, which are dangerous, are sometimes used to improve athletic performance. Is there a significant difference between the population proportions? State appropriate hypotheses for a significance test to answer this question. Define any parameters you use.

A random sample of 200 New York State voters included 88 Republicans, while a random sample of 300 California voters produced 141 Republicans. Which of the following represents the 95%confidence interval that should be used to estimate the true difference in the proportions of Republicans in New York State and California?

(a) (0.44-0.47)±1.96(0.44)(0.56)+(0.47)(0.53)200+300

(b) (0.44-0.47)±1.96(0.44)(0.56)200+(0.47)(0.53)300

(c) (0.44-0.47)±1.96(0.44)(0.56)200+(0.47)(0.53)300

(d)(0.44-0.47)±1.96(0.44)(0.56)+(0.47)(0.53)200+300

(e) (0.44-0.47)±1.96(045)(0.55)1200+1300
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