Determine the necessary sample size for the following examples: a. Salt is packa

Question

Determine the necessary sample size for the following examples:
a. Salt is packaged in 16 ounce bags. To test the weight of the bags, a few
were checked. The mean weight was 15.95 ounces and the standard
deviation is 0.5 ounces. The estimate should be within .02 ounces.
Assume a 93 percent confidence level.
b. A senator wants an estimate of the proportion of the population who
support her education views. She wants the estimate to be within .013 of
the true proportion. Assume a 95 percent level of confidence.
c. 45 percent of tourists going to Las Vegas go to a concert. The Las Vegas
tourism board wants to update this percentage. For the new study, the
estimate should be within 2% of the population proportion with a 98
percent confidence level.

Explanation / Answer

Ans:

a)z value for 93% CI is 1.81

Sample size required,n=1.81^2*0.5^2/0.02^2=2048

b)For 95% confidence interval,z=1.96

Margin of error=0.013

No prior estimate of p,So,condiser p=0.5

Sample size required,n=1.96^2*0.5*(1-0.5)/0.013^2=5683

c)For 98% confidence interval,z=2.326

Margin of error=0.02

prior estimate of p=0.45

Sample size required,n=2.326^2*0.45*(1-0.45)/0.02^2=3348

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