Question

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1. Construct the indicated confidence interval for the population mean μ using the​ t-distribution. Assume the population is normally distributed. c=0.99​, x=13.1​, s=3.0​, n= 6
2. Construct the indicated confidence interval for the population mean μ using the​ t-distribution. Assume the population is normally distributed. c=0.95​, x=14.5​, s=0.55​, n= 15
3. Use the given confidence interval to find the margin of error and the sample mean. (12.7​,19.9​The sample mean is
4. In a random sample of 18 people, the mean commute time to work was 30.9 minutes and the standard deviation was 7.2 minutes. Assume the population is normally distributed and use a​ t-distribution to construct a 99​% confidence interval for the population mean μ. What is the margin of error of μ​? Interpret the results.The confidence interval for the population mean μ is?
5. In a survey of 2565 adults, 1407 say they have started paying bills online in the last year. Construct a​ 99% confidence interval for the population proportion. Interpret the results.A​ 99% confidence interval for the population proportion is? Substitute the variables and solve for​ E, the margin of​ error, rounding to three decimal places.
6. A researcher wishes to​ estimate, with 95​% confidence, the population proportion of adults who think Congress is doing a good or excellent job. Her estimate must be accurate within 1​% of the true proportion.

(a) No preliminary estimate is available. Find the minimum sample size needed.

(b) Find the minimum sample size​ needed, using a prior study that found that 38​%

of the respondents said they think Congress is doing a good or excellent job.

(c) Compare the results from parts​ (a) and​ (b).

Answer 1

1)

Now , df=degrees of freedom=n-1=6-1=5

The critical value is ,

$t_{df,\alpha/2}=t_{5,0.01/2}=4.032$ ; From t-table

Therefore , the 99% confidence interval is ,

S X = tdf, 0/2 n

$13.1\pm 4.032*\frac{3.0}{\sqrt{6}}$

$13.1\pm 4.9382$