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13-07-2019

Product code Statistics-PH472

 

ANOVA, Chi-Square, and Binomial Tests

 

Complete all of the following problems prior to the Adobe Connect session. Please usethe Adobe Connection session to ask any questions you have and to check your answers.

 

  1. Analysis of Variance: A study was performed on fivesubjects to determine how environmental conditions such as temperature affect pulse. The fivesubjects were exposed to four different temperatures for 30 minutes before their pulse was taken. The data is recorded in the following table.

 

Perform an ANOVA test to determine whether or not pulse is affected by the external temperature. Use an α = 0.05. Reference Section 12.3 of Statistics for the Behavioral Sciences for assistance.

 

Temperature

Pulse (bpm)

40° F

82

81

98

90

75

60° F

68

74

92

88

72

80° F

71

69

90

87

70

100° F

78

75

97

92

73

 

 

  1. State the null hypothesis.

 

 

  1. State the alternative hypothesis.

 

 

  1. Calculate dfbetween (also known as dfNumerator).

 

 

  1. Calculate dfwithin (also known as dfDenominator).

 

 

  1. Use the values for dfN and dfD you calculated with an α = 0.05 to determine the expected F-ration. (Use Table B.4 “The FDistribution.”)

 

 

  1. Calculate the total (∑x) for each treatment condition (T).

 

 

  1. Calculate the sum of all scores in the research study (G=∑T).

 

 

  1. Calculate the sum of squares (SS) for each treatment conditions where:.

 

 

  1. Calculate SSTOTALwhere: .

 

 

  1. Calculate SSWITHIN where SSWITHIN=∑SSinside each treatment.

 

 

  1. Calculate SSBETWEEN where .

 

 

  • Calculate dfTOTAL.(Remember that you calculated dfBETWEEN and dfWITHIN in parts c and d.)

 

 

  1. Calculate MSBETWEENwhere MSBETWEEN = .

 

 

  • Calculate MSWITHINwhere MSWITHIN = .

 

 

  • Calculate the actual F-ration where F = .

 

 

  1. Based on the values you have calculated in this problem, should you accept or reject the null hypothesis?

 

 

  1. Based on your conclusion in part p, does temperature affect pulse rate based on this experiment?

 

 

  1. Chi-Square: Friedman and Roseman (1974) have suggested that personality type is related to heart disease. Specifically, Type A people, who are competitive, driven, pressured, and impatient, are more prone to heart disease. On the other hand, Type B individuals, who are less competitive and more relaxed, are less likely to have heart disease. The data is reported in the following table.

 

Perform a Chi-square test to determine whether or not there is a relationship between personality and heart disease. Use an alpha value of α = 0.05. Reference Section 17.3 and Demonstration 17.1 of Statistics for the Behavioral Sciences for assistance.

 

 

Heart

Vascular

Hypertension

None

Type A Personality

38

27

43

70

Type B Personality

22

23

17

120

 

 

  1. State the null hypothesis.

 

 

  1. State the alternative hypothesis.

 

 

  1. Calculate the degrees of freedom (df).

 

 

  1. Locate the critical region (Use Table B.8 “The Chi-Square Distribution.”)

 

 

  1. Calculate the row and column totals.Record your results in the following table:

 

 

Heart

Vascular

Hypertension

None

fc

Type A Personality

38

29

43

60

 

Type B Personality

18

22

14

126

 

fr

 

 

 

 

 

 

  1. Calculate n.

 

 

  1. Calculate the expected frequencies (fc) and record in the following table:

 

Personality

Disease

Type A Personality

 

Heart

 

Vascular

 

Hypertension

 

None

 

Type B Personality

 

Heart

 

Vascular

 

Hypertension

 

None

 

 

 

  1. Perform the calculations in the following table to calculate: .

 

 

 

Type A: Heart

38

 

 

 

 

Type A: Vascular

29

 

 

 

 

Type A: Hypertension

43

 

 

 

 

Type A: None

60

 

 

 

 

Type B: Heart

18

 

 

 

 

Type B: Vascular

22

 

 

 

 

Type B: Hypertension

14

 

 

 

 

Type B: None

126

 

 

 

 

 

 

  1. Calculate the chi-square statistic: .

 

 

  1. Based on the chi-square statistic you calculated above and the critical region that you determined earlier, should you accept or reject the null hypothesis?

 

 

  1. Based on your conclusion in part j, is there a connection between personality type and disease?

 

 

  1. Binomial Test: A new medication that is designed to decrease anxiety was tested on 87 individuals that have been diagnosed with chronic depression. After the study, 36 of the test subjects reported a noticeable decrease in their anxiety and the other 51 subjects reported that they had noticed no change in their anxiety levels.

 

Perform a binomial test on this dataset to determine whether or not the drug decreases anxiety in people with chronic depression. Reference Sections 18.1 and 18.2 of Statistics for the Behavioral Sciences for assistance.

 

  1. State the value on n (the total number of subjects).

 

 

  1. State the value X (the number of subjects who reported a decrease in anxiety).

 

 

  1. State the null hypothesis.

 

 

  1. State the alternative hypothesis.

 

 

  1. Find the critical region using an alpha value of 0.05. (Use Table B.1 “The Unit Normal Table.”)

 

 

  1. Calculate the z-score. (Use equation 18.1.)

 

 

  1. Given this result, do you reject the null hypothesis?

 

 

  1. Based on your conclusions, does this medication help to reduce the anxiety of patients with chronic depression?

 

 

Download Questions

a. State the null hypothesis. H0: ?1 = ?2 = ?3 ... = ?k b. State the alternative hypothesis. H1: Means are not all equal. c. Calculate dfbetween (also known as dfNumerator). 1.7 d. Calculate dfwithin (also known as dfDenominator). 2.3 e. Use the values for dfN and dfD you calculated with an ? = 0.05 to determine the expected F-ration. (Use Table B.4 “The FDistribution.”)

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