1) A study examined the change in pulse rates for a group of 31 individuals 'before' and 'after' exercise which involved running on the spot.

a)What is the absolute value of the t-statistic?

b)What are the degrees of freedom?

c)What is the p-value?

d)Do you reject or not reject the null hypothesis?

3) A population is normally distributed with a known standard deviation, = 15units. A random sample of size 36 is obtained from this population.The mean of this sample is 50.

a) What is the lower limit of the 95% confidence interval for

the population mean?

b) What is the upper limit of the 95% confidence interval for

the population mean?

4) A health and wellbeing committee claims that working an average of 40 hours per week is recommended for maintaining a good work-life balance. A random sample of 15 full-time employees were surveyed about how many hours they worked; the data are shown below. You may assume that the data come from a population that is normally distributed.

5) You are interested in finding out whether the hours employees work from home are similar between males and females. You randomly select 40 multinational companies and ask them to report average working from home hours for their male and female employees during March 2021. Would you use a two-sample t-test or a paired t-test for this data?

6) a) What is the value of b0?

b) What is the value of b1?

c) What is the se(b1)?

d) calculate the absolute value of the test statistic for b1.

e) What is the goodness of fit (as a percentage)?

f) What is the correlation?

g) Would you reject or not reject the hypothesis?

7) Consider a large clothing shop in Sydney. Suppose it is known that the number of business suits sold per day is normally distributed with a mean, = 23 and standard deviation, = 10.Mr Wood is employed to sell business suits. The number of business suits he sells each day for 40 days is recorded and the mean number per day calculated. What is the probability that Mr Wood's average daily sales will be more than 26 business suits?

8) For the plots above regarding a regression of the carcinogen PCB (polychlorinated biphenyl) versus age in a sample of trout, are all the assumptions met? Interpret residuals versus fits as you would residuals versus x. Select the best answer.

A)No, the histogram of the residuals is not sufficiently symmetric

B)No, the residuals are not evenly spread either side of the horizontal line for the range of x-values