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Chapter 10: Q. AP3.8 (page 702)

A beef rancher randomly sampled 42 cattle from her large herd to obtain a 95%confidence interval for the mean weight (in pounds) of the cattle in the herd. The interval obtained was (1010,1321). If the rancher had used a 98%confidence interval instead, the interval would have been

a. wider with less precision than the original estimate.

b. wider with more precision than the original estimate.

c. wider with the same precision as the original estimate.

d. narrower with less precision than the original estimate.

e. narrower with more precision than the original estimate.

Short Answer

Expert verified

The correct option is (a) Wider with less precision than the original estimate

Step by step solution

01

Given Information

We have to determine the interval If the rancher had used a 98%confidence interval instead .

02

Simplification

The confidence level rises when a 98percent confidence interval is used instead of a 95percent confidence interval.
As the confidence level rises, it is more likely that the confidence interval will contain the true mean, and as a result, the confidence interval will need to include all conceivable values for the mean, implying that the confidence interval will be bigger.
As the confidence interval widens, assessments such as confidence interval become more precise since the population mean has more plausible values.

Hence, the correct option is (a) Wider with less precision than the original estimate

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Most popular questions from this chapter

A large university is considering the establishment of a schoolwide recycling program. To gauge interest in the program by means of a questionnaire, the university takes separate random samples of undergraduate students, graduate students, faculty, and staff. This is an example of what type of sampling design?

a. Simple random sample

b. Stratified random sample

c. Convenience sample

d. Cluster sample

e. Randomized block design

A random sample of size n will be selected from a population, and the proportion p^3051526=0.200=20.0%p^ of those in the sample who have a Facebook page will be calculated. How would the margin of error for a 95% confidence interval be affected if the sample size were increased from 50to200 and the sample proportion of people who have a Facebook page is unchanged?

a. It remains the same.

b. It is multiplied by 2.

c. It is multiplied by 4.

d. It is divided by 2.

e. It is divided by 4.

Starting in the 1970s, medical technology has enabled babies with very low birth weight (VLBW, less than1500grams, or about 3.3 pounds) to survive without major handicaps. It was noticed that these children nonetheless had difficulties in school and as adults. A long-term study has followed 242 randomly selected VLBW babies to age 20years, along with a control group of 233 randomly selected babies from the same population who had normal birth weight. 50

a. Is this an experiment or an observational study? Why?

b. At age20,179 of the VLBW group and 193 of the control group had graduated from high school. Do these data provide convincing evidence at the 伪=0.05 significance level that the graduation rate among VLBW babies is less than for normal-birth-weight babies?

Does drying barley seeds in a kiln increase the yield of barley? A famous

experiment by William S. Gosset (who discovered the t distributions) investigated this

question. Eleven pairs of adjacent plots were marked out in a large field. For each pair,

regular barley seeds were planted in one plot and kiln-dried seeds were planted in the

other. A coin flip was used to determine which plot in each pair got the regular barley seed

and which got the kiln-dried seed. The following table displays the data on barley yield

(pound per acre) for each plot.

Do these data provide convincing evidence at the 伪=0.05 level

that drying barley seeds in a kiln increases the yield of barley, on average?

Literacy Refer to Exercise 2.

a. Find the probability that the proportion of graduates who pass the test is at most 0.20higher than the proportion of dropouts who pass, assuming that the researcher鈥檚 report is correct.

b. Suppose that the difference (Graduate 鈥� Dropout) in the sample proportions who pass the test is exactly 0.20. Based on your result in part (a), would this give you reason to doubt the researcher鈥檚 claim? Explain your reasoning.
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