Question

1. Are the following statements TRUE or FALSE?:

(a) According to the Central Limit Theorem, given a large sample size (N > 30), then a normal probability plot of the same data would necessarily follow a straight line.

(b) A 95% confidence interval for a population mean that does not include zero would also mean that a hypothesis test on the same data would yield a significant result at the .05 level.

(c) The mean of a t-distribution with 5 degrees of freedom is equal to the mean of a standard normal distribution.

(d) The sum of squared deviations from the mean is always equal to 0.

(e) The Empirical Rule is suitable for a t-distribution with 500 degrees of freedom.

(f) The standard deviation of the sampling distribution of x̄  is σ.

(g) A histogram is appropriate for summarizing data about political party affiliation.

(h) The degrees of freedom for a two-sample independent t-test is N – 2

Answer 1

a) False, the normal probability plot of the same data will be follow symmetric bell-shaped curve.

b) it's depend on the hypothesis that if H0: popln mean = 0 , and alternative hypothesis is two sided then hypothesis test on the same data would yield a significant result at the 0.05 level.

c) True, for n=5, mean = 0 and also for standard normal distribution mean = 0.

d) false,

e) true sense for lajane t distribution approaches to normal distribution.

f) false the standard deviation of the sampling distribution of x.bar = sigma/✓n

g) False, histogram is used to plot the frequency of score occurrences in a continuous data set that has been divided into classes. bar chart is best option here.

h) False, it is n1+n2-2