Question

A hospital is wanting to know whether or not they should serve caffeinated coffee in their waiting rooms.

The hospital tested 31 patients heart rates before coffee and then again after 2 cups of coffee.

You are asked to determine if there is sufficient evidence to show that caffeinated coffee increases heart rate.

1. Identify the claim. 2. State the null and alternative hypotheses, in words and in symbolic form. 3. Explain what type of test you will be performing (i.e. a test of two dependent means, a test for correlation, etc.) and why that test is appropriate to address the main question you are trying to answer. 4. Select the significance level and determine if it is a one or two-tailed test. 5. Identify the test statistic and compute the value of the test statistic and the p-value. 6. Make a decision of whether to Reject or Fail to Reject the null hypothesis. 7. Restate your decision in nontechnical terms. That means, state your conclusion in a way that anyone can understand; a final conclusion that just says “reject the null hypothesis” by itself without explanation is not helpful to those who hired you. Explain in ordinary terms what it means.

Heart Rate Before Coffee             Heart Rate After Coffee                                               

80           95                                                          

70           100                                                        

80           84                                                          

65           65                                                          

77           84                                                          

60           74                                                          

90           100                                                        

75           85                                                          

88           98                                                          

70           95                                                          

78           80                                                          

70           80                                                          

62           78                                                          

50           60                                                          

72           88                                                          

75           79                                                          

60           72                                                          

72           90                                                          

60           65                                                          

68           78                                                          

65           75                                                          

62           75                                                          

75           90                                                          

84           88                                                          

87           95                                                          

73           87                                                          

78           88                                                          

68           75                                                          

72           84                                                          

81           92                                                          

75           86

Answer 1

1)

Claim: caffeinated coffee increases heart rate.

2)

difference (d) = Heart Rate After Coffee - Heart Rate Before Coffee

Null Hypothesis:

OR caffeinated coffee does not increases heart rate.

Alternative Hypothesis:

OR caffeinated coffee increases heart rate.

3)

Test of two dependent mean or Paired T test.

4)

One tailed test (right)

5)

Computational table:

Calculation:

Test statistic:

Degrees of Freedom = n-1 = 31-1 = 30

P-value = 0.0000          ....Using t table

6)

P-value < α, i.e. 0.000 < 0.05, That is Reject Ho at 5% level of significance.

7)

There is sufficient evidence that caffeinated coffee increases heart rate.