Question

1. A sample of 96 observations showed an average of 25 and a standard deviation of 16. Construct the 90% confidence interval for the population mean. What is the lower limit of this interval? NOTE: WRITE YOUR ANSWER USING 4 DECIMAL DIGITS. DO NOT ROUND UP OR DOWN.

2. In a recent poll, from a sample of 140 likely voters, 65 answered they approve the way the president is handling his job. Compute the upper limit of the 95% confidence interval for the proportion of voters who approve the way the president is handling his job.  NOTE: WRITE YOUR ANSWER WITH 4 DECIMAL DIGITS. DO NOT ROUND UP OR DOWN.

3. If the population standard deviation of the lifetime of a light bulb is 100 hours, how large of a sample must be taken in order to be 95% confident that the margin of error will not exceed 15 hours?

Answer 1

1). given data are:-

df = (n-1) = (96-1) = 95

t critical value for alpha=0.10,df = 95, both tailed test be:-

the 90% confidence interval for the population mean is :-

the lower limit of this interval = 22.2875

2).given data and necessary calculations are:-

sample size (n) = 140

sample proportion () =64/140 = 0.464286

z critical value for 95% confidence interval both atiled test be:-

the 95% confidence interval be:-

the upper limit of the 95% confidence interval for the proportion of voters who approve the way the president is handling his job = 0.5469

3).given data are:-

the needed sample size be:-

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