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Chapter 7: Q.6 (page 460)

A researcher initially plans to take anSRS of size n from a population that has a mean of 80 and a standard deviation of 20. If he were to double his sample size (to 2n), the standard deviation of the sampling distribution of the sample mean would be multiplied by

(a) 2.

(b)12 .

(c) 2.

(d) 12.

(e)12n

Short Answer

Expert verified

The correct answer is(b)

Step by step solution

01

Given Information

From the given data, we have,

μx=μ=80σ-x=σn=20

02

Explanation

Given the sample size is doubled. So nbecomes 2n.

New Standard deviation of the sample distribution is,

localid="1650261481655" σx=σ2n=12σn

Hence the answer is (b)

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Most popular questions from this chapter

The central limit theorem is important in statistics because it allows us to use the Normal distribution to make inferences concerning the population mean

(a) if the sample size is reasonably large (for any population).

(b) if the population is normally distributed and the sample size is reasonably large.

(c) if the population is normally distributed (for any sample size).

(d) if the population is normally distributed and the population variance is known (for any sample size).

(e) if the population size is reasonably large (whether the population distribution is known or not,

Increasing the sample size of an opinion poll will

(a) reduce the bias of the poll result.

(b) reduce the variability of the poll result.

(c) reduce the effect of nonresponse on the poll.

(d) reduce the variability of opinions.

(e) all of the above.

Scrabble In the game of Scrabble, each player begins by drawing 7 tiles from a bag containing 100 tiles. There are 42 vowels, 56 consonants, and 2 blank tiles in the bag. Cait chooses an SRS of 7 tiles. Let p^be the proportion of vowels in her sample.

(a) Is the 10%condition met in this case? Justify your answer.

(b) Is the Normal condition met in this case? Justify your answer.

For Exercises 1 to 4, identify the population, the parameter, the sample, and the statistic in each setting

Hot turkey Tom is cooking a large turkey breast for a holiday meal. He wants to be sure that the turkey is safe to eat, which requires a minimum internal temperature of 165°F. Tom uses a thermometer to measure the temperature of the turkey meat at four randomly chosen points. The minimum reading in the sample is 170°F

The histogram above left shows the intervals (in minutes) between eruptions of the Old Faithful geyser for all 222recorded eruptions during a particular month. For this population, the median is 75minutes. We used Fathom software to take 500SRSs of size 10from the population. The 500values of the sample median are displayed in the histogram above right. The mean of the 500sample median values is 73.5.

Suppose we had taken samples of size 20instead of size 10. Would the spread of the sampling distribution be larger, smaller, or about the same? Justify your answer

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