A random sample of 100 observations from a normally distributed population posse

Question

A random sample of 100 observations from a normally distributed population possesses a mean equal to 91.2 and a standard deviation equal to 63. Use this informaton tocomplete parts a through ebelow. a Find a 95% confidence interval for Round to two decimal places as needed. b, What do you mean when you say that a confidence coefficient is 0.96? O A. A coefficient of 0.96 means that there is a probability of 0.95 that an interval estimator constructed using this coeficient wil enclose the population parameter confidence O B. A confidence coefficient of 0.95 means that there is a probability of 0.95 that an interval estimator constructed using this coefficient will contain all of the values in the relevant sample, O c. A confidence coefficient of 0.96 means that 95% of the values in any sample taken from the population wil be contained in an intervalestimator constructed using this coefficient. O D. A confidence coefficient of 0.95 means that 95% of the values in the population wilbe contained in an interval estimator constructed using this coefficient. Find a 99% confidence interval for w. (Round to two decimal places as needed.) d. What happens to the width of a confidence interval as the value of the confidence ooefsoient is increased while the sample size is held fxed? Increasing the confidence coefficient while keeping the sample size fixed wil cause in the This means that the width of the confidence interval wil e. Would your confidenoe intervals of parts a and c be valid if the distribution of the original population were not normal? Explain. OA Yos, since the sample sizes are large n230, the condison guarantees that the samping distribution of x is approximately normal. O B. Yos sroe he sample was randomly selected Mom he target population, the disteuson ofx is guaranteed to be approximately normal. sampling oc re mpde sees are large and randomly selected from the target populaton that the sampling No the underlvino distributon must be nomal confdenceintervals of x is

Explanation / Answer

Solution:-

Given,

N = 100,

Mean = 91.2

Standard deviation = 6.3

Calculation

M = 91.2
t = 1.96
sM = (6.32/100) = 0.63

= M ± Z(sM)
= 91.2 ± 1.96*0.63
= 91.2 ± 1.235

95% CI [89.965, 92.435]

You can be 95% confident that the population mean () falls between 89.965 and 92.435

Calculation

M = 91.2
t = 2.58
sM = (6.32/100) = 0.63

= M ± Z(sM)
= 91.2 ± 2.58*0.63
= 91.2 ± 1.623

99% CI [89.577, 92.823].

You can be 99% confident that the population mean () falls between 89.577 and 92.823.

Decreasing the sample size causes the error bound to increase, making the confidence interval wider.

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