02 hw | Business & Finance homework help

For estimating an interval that will contain the true population mean, we can use confidence intervals. Confidence intervals provide a range of values that is likely to contain the true population mean with a certain degree of certainty, usually 95%. The formula for calculating this type of interval is: x ̅ ± (z * \sqrt{\frac{s^{2}}{n}}) where x ̅ represents the sample mean, z represents the critical value from a standard normal distribution for the desired level of confidence, s^2 represents sample variance and n represents sample size.

For estimating an interval that will contain the true population proportion, we can use proportions confidence intervals. Proportions confidence intervals provide a range of values that is likely to contain the true population proportion with a certain degree of certainty, usually 95%. The formula for calculating this type of interval is: p ± (z * \sqrt{\frac{p(1-p)}{n}}) where p represents sample proportion, z represents the critical value from a standard normal distribution for desired level of confidence and n represent sample size.

Finally, for estimating an interval that will contain population variance we can use chi-square test. Chi-square tests are used to compare observed frequencies in one or more categories against expected frequencies in those same categories. The formula used to calculate these types of intervals is χ^2 = Σ [ (O – E)* 2 ]/E where O stands observed frequency and E stands expected frequency.