Question

In this project you will be asked to find confidence interval and perform a hypothesis test for the mean of one population.

Be sure to show all your work neatly.

Instructions

The table provided below contains pulse rates after running for 1 minute, collected from females who drink alcohol ("Pulse rates before," 2013). The mean pulse rate after running for 1 minute of females who do not drink is 97 beats per minute. Do the data show that the mean pulse rate of females who do drink alcohol is higher than the mean pulse rate of females who do not drink? Test at the 5% level.

Pulse Rates of Woman Who Use Alcohol

176	150	150	115	129	160
120	125	89	132	120	120
68	87	88	72	77	84
92	80	60	67	59	64
88	74	68

1. What is the appropriate test for this case?                                                                                                                 (5 points)
2. What are the assumptions to run the test?                                                                                                                (10 points)
3. What is the null hypothesis?                                                                                                                             (5 points)
4. What is the alternative hypothesis?                                                                                                              (5 points)
5. Determine if this test is left-tailed, right-tailed, or two-tailed.                                                           (5 points)
6. What is the significance level?                                                                                                                         (5 points)
7. What is the test statistics?                                                                                                                                                 (5 points)
8. What is the p-value?                                                                                                                                            (10 points)
1. Do we reject the null hypothesis? Why?                                                                                                     (10 points)
10. What is the conclusion?                                                                                                                                     (10 points)
11. What is 95% confidence interval for the population mean?                                                                (10 points)
50. Interpret the confidence interval.                                                                                                                  (10 points)

Answer 1

Hypothesised population mean, =97

Sample size, n =27

Degrees of freedom, df =n - 1 =27 - 1 =26

Sample mean, = =100.52

Sample std.deviation, s = =33.5609

Standard Error, SE =s/ =33.5609/ =6.46

a.

The appropriate test is one sample t-test because the sample size, n < 30 and also the population standard deviation, is unknown.

b.

Assumptions:

1) The dependent variable must be continuous, i.e., interval or ratio.

2) The observations are independent of one another.

3) The dependent variable should be normally or approximately normally distributed.

4) The dependent variable should not have any outliers.

c.

Null Hypothesis, H0:

The mean pulse rate of females who do drink alcohol is not significantly higher than the mean pulse rate of females who do not drink. 97

d.

Alternative Hypothesis, H1:

The mean pulse rate of females who do drink alcohol is significantly higher than the mean pulse rate of females who do not drink. > 97

e.

This is a right-tailed test because we want to determine if the population mean pulse rate of females who do drink alcohol is higher than the hypothesised population mean of 97.

f.

Significance level, =5% =0.05

g.

Test statistic, t =(​​​​​​)/SE =(100.52 - 97)/6.46 =0.5449

h.

For a right-tailed test, at df =26, the p-value for the test statistic, t =0.5449 is: p-value =0.2952

i.

We do not reject the null hypothesis because p-value of 0.2952 > 0.05 significance level.

j.

Conclusion:

We do not have sufficient statistical evidence to claim that the mean pulse rate of females who do drink alcohol is higher than the mean pulse rate of females who do not drink.

k.

At 95% confidence level, for a two-tailed case, t-critical =2.06

Margin of Error, MoE =t-critical*SE =2.06*6.46 =13.31

Two-sided 95% confidence interval for the population mean, =MoE =100.5213.31 =[87.21, 113.83].

l.

Interpretation:

We are 95% confident that the interval [87.21, 113.83] contains the true population mean pulse rate, of females who do drink alcohol.