Question

(4.1)

A random sample of 89 observations produced a mean x = 26.1 and a standard deviation s = 2.4

a. Find a? 95% confidence interval for ?.

b. Find a? 90% confidence interval for ?.

c. Find a? 99% confidence interval for ?.

a. The? 95% confidence interval is (----,----) ?(Use integers or decimals for any numbers in the expression. Round to two decimal places as? needed.)

b. The? 90% confidence interval is ----,------. (Use integers or decimals for any numbers in the expression. Round to two decimal places as? needed.)
c. The 99% confidence interval is ...,….. (Use integers or decimals for any numbers in the expression. Round to two decimal places as? needed.)

(4.2)

The mean and standard deviation of a random sample of n measurements are equal to 34.8

and 3.4?, respectively.

a. Find a 95?% confidence interval for ? if 121.

b. Find a 95?% confidence interval for ? if n = 484.

c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient? fixed?

a. The 95?% confidence interval for ? if n = 121 is approximately (-------) ?(Round to three decimal places as? needed.)

b. Find a 95?% confidence interval for ? if n = 484 (--------) ?(Round to three decimal places as? needed.)

c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient? fixed? (----------) (Round to three decimal places as? needed.)

Answer 1

• A)The 95% confidence interval is given by
• The critical value at Z_a/2=Z_0.025 is 1.96
• 0.95=P(-1.96<N(0,1)<1.96)
• 0.95=P(-1.96<<1.96)
• The Margin of error is given by
• m.g=critical value *standard error
• =1.96*(2.4*sqrt(89))
• =0.4986
• By substituting the calculated values
• the confidence interval obtained is
• (25.601<<26.59)
• B)The 90%confidence interval is given by
• The critical value at Z_a/2=Z_0.05 is 1.645
• 0.95=P(-1.645<N(0,1)<1.645)
• 0.95=P(-1.645<<1.645)
• The Margin of error is given by
• m.g=critical value *standard error
• =1.645*(2.4*sqrt(89))
• =0.4184
• By substituting the calculated values
• the confidence interval obtained is
• (25.681<<26.51)
• C)To calculate the 99% confidence interval.
• he critical value at Z_a/2=Z_0.005 is 2.5758
• 0.95=P(-2.5758<N(0,1)<2.5758)
• 0.95=P(-2.5758<<2.5758)
• The Margin of error is given by
• m.g=critical value *standard error
• =2.5758*(2.4*sqrt(89))
• =0.65528
• By substituting the calculated values
• the confidence interval obtained is
• (25.444<<26.752)