Statistics: true/false?

Question

a. A one-sided test is used whenever the sample size is small.

b. If alpha = .05, it means that if Ho is true, the chance of falsely rejecting it is maximum 5%.

c. If the P-value is .04, and the significance level alpha = .05, then we will reject Ho.

d. A hypothesis test is performed, and the data were found to be statistically significant at alpha = 5%. Then data will be significant at 1% also.

e. Increasing alpha increases the critical value.

f. Decrreasing alpha increases the area of the critical region.

Answer 1

a. False. Whether we use a one- or two-sided test depends on the nature of the question we are asking (via the alternative hypothesis we construct) and has nothing to do with the sample size.

b. True, though not directly. Directly it means that we reject H0 for data which would only be seen in 5% or fewer of cases where H0 is true. So if H0 is true, only 5% or fewer of samples (on average) will cause us to reject H0. So the chance of falsely rejecting H0 is 5% or less.

c. True. We reject H0 when the p-value is less than α.

d. False. The probability of observing the given data, if H0 is true, is less than 5%, but may not be less than 1%.

e. False; depends on the test statistic. True for p-value.

f. False. As we decrease α it is harder to reject H0, and so the region of values for which we will reject it (i.e. the critical region) decreases in area.