The overall distance traveled by a golf ball is tested by hitting the ball with Iron Byron, a mechanical golfer with a swing that is said to emulate the distance hit by the legendary champion, Byron Nelson. Ten randomly selected balls of two different brands are tested and the overall distance measured. The data follow:
Brand 1: 275, 286, 287, 271, 283, 271, 279, 275, 263, 267
Brand 2: 258, 244, 260, 265, 273, 281, 271, 270, 263, 268.
a. Is there evidence that overall distance is approximately normally distributed? Is an assumption of equal variances justified?
b. Test the hypothesis that both brands of ball have equal mean overall distance. Use α = 0.05. What is the P-value?
c. Construct a 95% two-sided CI on the mean difference in overall distance for the two brands of golf balls.
d. What is the power of the statistical test in part (b) to detect a true difference in mean overall distance of 5 yards?
e. What sample size would be required to detect a true difference in mean overall distance of 3 yards with power of approximately 0.75?

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.

b) 1/3 * 1/5

step-by-step explanation:

each smallest part is 1/15 since the written one is 1/5 and it's divided by 3 equal parts. (1/5 )/3 = 1/15 = 1/3 * 1/5

if the probability is 1/12, 75 people will receive a $25 gift card

step-by-step explanation: