Honors Assignment 1 Honors Assignment 1 Goal: To test the hypothesis that the resting mean rate of men in the age group 35-45 is greater than 55 beats per minute. Explanation: The resting hear rate of the body (commonly called RHR) is the number of contractions of the heart that occur in the single minute while the body is at complete rest. Procedure: We will collect the sample of 30 men in the age group of 35-45 and calculate the resting heart rate using finger and stopwatch. An analysis of the resting heart rate shows the mean of resting heart rate is 53.16.The population standard deviation is 5 betas/minute. A research claim that for the healthy heart the resting hear beat range must be greater than 48 and less than 60.So we will conduct hypothesis testing in this range. Data: Below is the data of the 30 men collected for the resting heart beat rate Person 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Number of RHB/minute 48 46 54 55 57 59 50 54 53 52 50 47 55 58 55 60 52 Honors Assignment 1 18 19 20 21 22 23 24 25 26 27 28 29 30 52 47 52 51 56 48 54 57 58 50 60 53 52 Descriptive Statistics of the data are below Column1 Column2 Column1 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 53.16666667 0.716125163 53 52 3.922379058 15.38505747 -0.751267968 -0.005033914 14 46 60 1595 30 Calculating the mean and standard deviation of the sample Honors Assignment 1 Mean=Sum of all heart beat/Total people =53.16 Standard deviation =3.9923 Standard error =.7161 Calculating the 95% confidence interval of the sample We have the critical value at the 95% confidence interval =1.96 Confidence interval is given by the formula = M=mean =53.16 Population standard deviation=5 Zc=1.96 Therefore the 95% confidence interval =(51.37,54.95) Thus the lower limit is 51.37 and the upper limit is 54.95. Hypothesis Testing: Null Hypothesis: Mean resting heart rate is m<=48 and m>=60 Alternative Hypothesis: Mean resting heart rate is 4848 Honors Assignment 1 Using excel the result is Z Test of Hypothesis for the Mean Data Null Hypothesis = Level of Significance Population Standard Deviation Sample Size Sample Mean Intermediate Calculations Standard Error of the Mean Z Test Statistic Upper-Tail Test Upper Critical Value p-Value 48 0.05 5 30 51.36 0.912 9 3.680 7 1.644 9 0.000 1 Reject the null hypothesis Thus from the above hypothesis it is clear that the resting heart rate is greater than 48. Next testing the claim that the resting heart rate is less than 60. Null Hypothesis: Resting heart rate ,m>=60 Alternative Hypothesis: Resting heart rate is <60 using excel conducting the hypothesis z test of for mean data null level significance population standard deviation sample size intermediate calculations 60 0.05 5 30 53.16 honors assignment 1 error statistic lower-tail lower critical value p-value 0.912 9 7.492 8 1.644 0.000 0 reject thus from here also claim is true that resting heart rate normal less than 60. conclusion above two step it becomes clear hear in age group 36-45 lie range 48-60. \fthis sheet undertakes project's testing person 2 3 4 6 7 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 summary statistics number rhb minute 48 46 54 55 57 59 50 53 52 47 58 51 56 observations minimum maximum confidence interval 53.167 3.922 input alpha 0.5 * z(1 - 0.5*alpha) z(0.5*alpha) 0.95 0.025 0.716 1.96 -1.96 limit upper 51.763 54.57 i will be delayed submitting final draft this project because needto attend some urgent matter on my side. nonetheless, rest assured submit as soon possible. 1. introduction purpose two-fold: average (measured ) men aged between 35 45 years at least beats per minute; and determine 95% containing men. (rhr) contractions a body rest. 2. table 1: descriptive median 53.000 mode 52.000 variance 15.385 kurtosis -0.751 skewness -0.005 14.000 sum count 1595 3. 4. 5. concluding remarks appendix possible today. calculated follows: midpoint ordered set. data, middle lies th observation 16th observation. since both 15th are 53, follows 53. s x n ... what follows, assume following: o normally distributed; good estimate given large size. thus: 1.404 54.570 hypothesis: greater or equal 55. alternative statistic: 2.56>