Question

1. If a two-sided t- test is run and the t-stat=2.20, we definitely reject H₀ at α=0.05 T/F

2. If we run a one-sample t-test and get a t-stat=6.74, with n=7, the p-value under one-sided conditions is:

3. For which of the following hypothetical scenarios is a binomial distribution most acceptable?

	a.	Surveying former smokers and asking them whether or not they have emphysema.
	b.	Finding out if there is a significant difference between the blood pressures of people who work in high-stress environments compared to those who work in low-stress environments.
	c.	Determining which stage of cancer (I, II, III, IV) patients should be categorized into.
	d.	Measuring the height of children at age five.

4. True or False: For a given t-stat and degrees of freedom, two-sided p-values are larger than one-sided p-value

5. If a t-test is run and t=2.56, then it is appropriate to assume that a significant result was found at α=0.05 T/F

6. Suppose that an individual (Mr. Armstrong) spent eight days in the gym this month. Below is the length of time (in minutes) that he spent exercising on each visit. 62    34    50    40    58    48    38    60

Assuming that the IQR is calculated as 20, which of the following data points should be considered an outlier?

a) 50

b) 38

c) 60

d) 62

Answer 1

Solution:

1) Given: Two- sided t test is used, t-stat = 2.20, alpha=0.05

Now tabulated value of t at 0.05 differs for different value of sample size ie; t at (n-1) d. f. Hence, it depends on the following criteria,

If cal |t |> tab t, then reject H0 else accept H0.

Hence the statement ,if a two-sided t- test is run and the t-stat=2.20, we definitely reject H0 at α=0.05 is False.

2) Given: t-stat = 6.74, n=7

To find : p-value at 6 d. F

From t-table for single tail we see if we go along the row 6 the p-value lies between 0.0005 and 0.00025.

However, if we want exact p-value use any software and value comes out to be 0.00026.

3) For the following situation Binomial distribution will be most acceptable:

Surveying former smokers and asking them whether or not they have emphysema.

Since Binomial distribution has only two outcomes - success and failure.

4) For a given t-stat and degrees of freedom, two-sided p-values are larger than one-sided p-value- True

Since, the significant values of t at level of significance Alpha for a single- tailed test can be obtained from those of two- tailed test by looking the values at level of significance 2*alpha.

5) False, since the values at different significant levels can also be in the range of 2.56.

6) 62 can be considered as an outlier. Using five- point summary.