State whether the following statements are True or False 5 m

State whether the following statements are True or False. (5 marks, 1 Mark Each) 1. A Type II error is rejecting a true null hypothesis. 2. When testing a null hypothesis about a single population mean and the population standard deviation is unknown, if the sample size is less than 30, one compares the computed test statistic for significance with a value from the Z- distribution. 3. As the level of significance decreases, we are more likely to fail to reject the null hypothesis. 4. For a hypothesis test about a population proportion or mean, if the level of significance is greater than the p-value, fail to reject null the null hypothesis. 5. If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations, the variances are pooled to compute the best estimated variance.

Solution

Solutions: (With Reasons)

1) False

A Type II error can only occur if the null hypothesis is false.

2) False

If sample sie is <30 , t test is required.

3) True

As level of significance decreases , chances of P-value > alpha increases.

4) False

If the level of significance is greater than the p-value, reject the null hypothesis.

5) True