Question

In this assignment, you will use the method of comparing confidence intervals to test for a significant difference between the resting heart rate of males and females. You have observed that the mean rates are not exactly the same but are they significantly different?

Steps

1. Open your Unit 5 assignment and identify the means and confidence intervals you calculated for male-at-rest and female-at-rest.
2. Use the 95% confidence intervals to determine if the resting male heart is the same as the resting female heart.
3. Write the null hypothesis being tested and whether you reject the null hypothesis based on the comparison of confidence intervals. Refer to the RealizeIt lesson for information on using confidence intervals to test a hypothesis.

Additional Instructions:

Your assignment should be typed into a Word or other word processing document, formatted in APA style. The assignments must include

• Running head
• A title page with
  • Assignment name
  • Your name
  • Professor’s name
  • Course

Heart rate before and after exercise      
M=0 F=1   Resting   After Exercise
0   85.9   87.5
0   67.7   79.4
0   80.3   93.4
0   85.2   97.7
0   86.3   99.7
0   76.6   83.7
0   94.4   101.9
0   86.4   100.6
0   83.4   97.4
0   89.8   97.4
0   88.7   97.1
0   78.4   87.2
0   71.3   79.9
0   92.6   104.7
0   86.2   95.9
0   83.9   93.9
0   78.1   90.1
0   64   70.7
0   72.8   86.7
0   72.7   81.2
0   80.2   83.3
0   78.2   86
0   70.6   90.2
0   75.5   84.4
0   82.7   94.2
0   87.7   95.1
0   80   88.7
0   73.4   82.7
0   89.5   94.6
0   77.6   84.6
0   76.6   86.4
0   85.6   96.2
0   74.2   82.1
0   79   91.6
0   74.6   86.7
0   88.8   98.8
0   82.1   85.6
0   77.6   80.6
0   77.9   83.8
0   88.1   93.9
0   81.6   90.3
0   91.2   100.6
0   80.3   88
0   76.7   91.8
0   88.4   103
0   75.2   86.5
0   75.2   84.9
0   73.1   71.9
0   77   84.7
0   59   68.2
0   84.9   96
0   87.5   105.9
0   75.6   84.3
0   84   90.4
0   78.2   94
0   86.6   90.6
0   84.9   95.1
0   78.8   90.4
0   69.4   82.6
0   78.3   91.1
0   76.9   92.3
0   84.2   87.9
0   76.3   85.9
0   86.3   99.7
0   72.3   80.9
0   81.8   93.8
0   92.8   99.8
0   74.8   90.2
0   91.7   99.2
0   71   87
0   96.1   100.2
0   82.5   95.1
0   81.9   97.5
0   89.7   94.8
0   81.4   100.9
0   74.8   94
0   88.1   102.1
0   69.2   81.4
0   78.8   90.9
0   85.3   94.2
0   74.8   81.3
0   77.7   89.9
0   78   89.8
0   80.5   95.3
0   75.4   84.8
0   81.5   84.2
0   73.9   85.2
0   69.4   74.1
0   89.4   96.7
0   70.9   82
0   82.9   90.2
0   89.6   106.7
0   74.5   75.6
0   92.3   102.2
0   87.7   98
0   78.9   89.7
0   79.8   81.5
0   85.5   97.4
0   87.3   94.1
0   77.8   97.8
0   71   80.1
0   82.5   90.7
0   74.8   83.7
0   69.2   79.4
0   80.5   87.4
0   89.4   99.2
0   74.5   88
0   85.5   92
1   76.6   88.2
1   79.2   90.4
1   80.6   101.3
1   75.5   93.1
1   83.9   90.5
1   73.9   89.1
1   76.8   90.8
1   85.2   93.5
1   82.1   93.5
1   76.3   87
1   97   104.5
1   81.5   86.5
1   65.3   86.3
1   80.8   86.7
1   78.5   89.9
1   86.3   97.6
1   89.8   92.9
1   87.8   98.5
1   76.2   89.9
1   74.2   88.8
1   67.4   78.8
1   75.5   80.2
1   80   90.2
1   76.4   88
1   94.9   95.7
1   89.2   96.9
1   83.3   87.7
1   85.8   90.4
1   75.3   84.1
1   77.9   99
1   70   83
1   88   94.2
1   86.9   95
1   87.1   95.9
1   79.3   82.7
1   81.2   90.7
1   82.9   91.9
1   87.4   103.6
1   83   90
1   76.8   83.3
1   76.9   87.7
1   79.8   88.2
1   83.2   93
1   79.5   88.6
1   82.4   89.3
1   80.8   84.2
1   83.2   94.5
1   71.6   81.5
1   82.8   93.1
1   76.8   92.8
1   93.2   100.4
1   91.4   100.9
1   97.3   103.3
1   88.3   90.1
1   80.6   85.2
1   87.4   91.7
1   96.5   99.3
1   77.9   91.6
1   76.1   84.1
1   85.2   89.7
1   68.6   72.8
1   79.4   92
1   85.2   99.2
1   74.3   85.6
1   74.3   89.2
1   78.5   98.5
1   80.4   90.8
1   82.9   85.9
1   78.9   90.7
1   78.6   87
1   87.5   93.9
1   78.9   91.4
1   80   89.1
1   80.4   89.2
1   88.3   93.5
1   80.6   95.9
1   85.8   90.5
1   84.6   93
1   80.5   91.8
1   92.4   101.2
1   84.4   96.7
1   82.3   86.9
1   77.2   85.8
1   83.3   82.1
1   86.2   98.9
1   81.3   97.7
1   90.2   96.4
1   78.4   85.5
1   84.7   101.6
1   89.7   94.3
1   78.4   88
1   79.9   88.5

Answer 1

Soln

From the data, we calculate the mean and standard deviation of the two groups for Resting.

Mean (X bar) = Sum of Values /n

and

Group 1 (Male)

Mean (x₁) = 80.39

Std Dev (s₁) = 7.05

n₁ = 108

Group 2 (Female)

Mean (x₂) = 81.77

Std Dev (s₂) = 6.27

n₂ = 92

alpha = 0.05

Z_Critical = 1.96

Null and Alternate Hypothesis

H₀: µ₁ = µ₂ (Mean Heart Rate is same for both Males and Female)

H_a: µ₁ <> µ₂ (Mean Heart Rate is not same for both Males and Female)

Test Statistic

Assuming, the population std deviation is not same.

t = (X_{1 ­­­}– X_{2 ­}– (µ₁ - µ₂))/ (s₁²/n₁ + s₂²/n₂ )^1/2 = -1.47

95% CI for Difference of Means = (X_{1 ­­­}– X_{2 ­}) +/- Z_Critical *(s₁²/n₁ + s₂²/n₂ )^1/2 = {-3.23, 0.46}

P-value = TDIST(1.47,108+92-2,2) = 0.143

Result

Since the test statistic lies in the 95% CI, we fail to reject the null hypothesis.

Conclusion

Rested Mean Heart Rate is same for both Males and Female