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StatisticsQ&A LibraryanN.49 Abstainers The Harvard study mentioned in the previ-fous exercise estimated that 19 % of college students ab-stain from drinking alcohol. To estimate this proportion inyour school, how large a random sample would you needto estimate it to within 0.05 with probability 0.95, if beforeconducting the studyC8.55 Vunwilling to guess the proportion value ata. You areyour school?h. You use the Harvard study as a guideline?Use the results from parts a and b to explain whystrategy (a) is inefficient if you are quite sure you'll geta sample proportion that is far from 0.50.SS0).ityS8.50 How many businesses fail?mate the proportion of businesses started in the year 2006that had failed within five years of their start-up. Howlarge a sample size is needed to guarantee estimating thisproportion correct to withina. 0.10 with probability 0.95?b. 0.05 with probability 0.95?c. 0.05 with probability 0.99?d. Compare sample sizes for parts a and b, and b and c,and summarize the effects of decreasing the margin oferror and incre asing the confidence level.851 Canada and the death penalty1998 indicated that 48% of Canadians favor imposingthe death penalty (Canada does not have it). A report byAmnesty International on this and related polls (www.amnesty.ca) did not report the sample size but stated,"Polls of this size are considered to be accurate within2.5 percentage points 95% of the time." About how largewas the sample size?8.52 Farm size An estimate is needed of the mean acreageof farms in Ontario, Canada. A 95% confidence intervalshould have a margin of error of 25 acres. A study 10heA study is planned to esti-onheеа8.56ntsTRYeninf aor"plehatelyataledA poll in Canada inen8.57anvelofyearsagoor 200 acres for farm size.a. About houin this province had a sample standard deviation8.58mmnle of farms is needed?Question

Asked Nov 8, 2019

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8.50 D

Step 1

(a)

Step-by-step procedure to obtain the value of *z* using MINITAB:

- Choose
**Graph > Probability Distribution Plot**choose**View Probability****> OK.** - From
**Distribution**, choose ‘**Normal**’ distribution. - Click the
**Shaded Area** - Choose
**Probability**and**Both Tail**for the region of the curve to shade. - Enter the
**Probability****value**as**05**. - Click
**OK**.

Output using the MINITAB software is given below:

Step 2

From the output, the value of *z* is 1.96 for 95% confidence.

Here, there is no information about the population parameter. Hence, use the conservative estimate π=0.5.

The sample size is obtained as follows:

Step 3

Thus, the required sample size is **97**.

(b)

The sample si...

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