For each of the following statements write \"T\" if you think it is right or \"F

Question

For each of the following statements write "T" if you think it is right or "F" otherwise. We can reduce the width of a confidence interval by increasing the confidence level. The sample mean is an unbiased point estimator of the population mean. As the sample size n increases, the T distribution approaches the standard normal distribution. The probability of making a Type I error is the significance level a, and is the probability of rejecting a true null hypothesis. In simple linear regression analysis, if the coefficient of determination is 1.0, then the independent variable and the dependent variable have a perfect correlation. For each of the following questions select one and only one choice (A, B, C, or D) you consider the best presented. In a two-tailed z test, the null hypothesis is rejected at the 0.05 level of significance, but cannot be rejected at the 0.02 level. The most accurate statement about the absolute value of the z statistic for this test is A |z-statistic| > 1.645 B 0

Explanation / Answer

Section I

#1 False, The higher level confidence interval would be wider (larger margin of error) than the lower level confidence interval, because it allows one to be more confident that the unknown population parameter is contained within the interval.

#2 True

#3 True

#4 True

#5 True

Section II

#1 For 0.05 significance level, the critical value of z is ±1.96 and for 0.02 significance level, the critical value of z is ±2.33. Therefore, correct option is C 1.96 < |z-statistic| < 2.33.

#2 Overall pattern shows negative slope and points follow a straight line pattern. Therefore, correct option is  B a strong negative linear relationship.

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