Question

In: Statistics and Probability

Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and...

Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and Population 2 does not. The data from these two samples is given below:

Population 1: 70, 70, 71, 71, 70, 71, 62

Population 2: 69, 75, 75, 72, 75, 68, 70, 72

Is there evidence, at an ?=0.05
α
=
0.05
level of significance, to conclude that there those who exercise regularly have lower resting heart rates? (Assume that the population variances are equal.) Carry out an appropriate hypothesis test, filling in the information requested.

A. The value of the standardized test statistic:

B. The p-value is

D. Your decision for the hypothesis test:

A. Do Not Reject ?0
H
0
.
B. Reject ?1
H
1
.
C. Do Not Reject ?1
H
1
.
D. Reject ?0
H
0
.

Solutions

Expert Solution

Answer:

Given that,

Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and Population 2 does not.

The data from these two samples are given below:

Population 1:

70, 70, 71, 71, 70, 71, 62

Population 2:

69, 75, 75, 72, 75, 68, 70, 72

Is there evidence, at an =0.05 level of significance.

To conclude that there those who exercise regularly have lower resting heart rates? (Assume that the population variances are equal.) Carry out an appropriate hypothesis test, filling in the information requested:

Hypothesis test:

Null hypothesis:

Alternative hypothesis:

Calculation table for population 1:

Mean ():

=485/7

=69.2857

Standard Deviation ():

=(70 - 69.2857)2 + ... + (62 - 69.2857)2/7

=63.42857/7

=9.06122449

=√9.06122449

= 3.010186787

=3.0102 (Approximately)

Population 1
69.2857
3.0102
7

Calculation table for population 2:

Mean ():

=576/8

=72

Standard Deviation ():

=(69 - 72)2 + ... + (72 - 72)2/8

=56/8

=7

=√7

= 2.64575131

=2.6458 (Approximately)

Population 2
72
2.6458
8

Point estimate= -

=69.2857-72

=-2.7143

Degree of freedom (df)=min (,)-1

=min(7,8)-1

=6

For 0.05 level of significance, left tail and 6 df, the critical value is t=-1.943

Decision rule:

Reject if test statistic t < 1.943

Standard Error (SE):

=1.47295621

=1.4729

Test stat t

[Since, ]

=-2.7143/1.4729

=-1.8428

The p-value:

The p-value is 0.0575.

The result is not significant at p < 0.05.

From above:

(A). Test statistic t =-1.8428

(B) p-value =0.0575

(C). Since p-value < 0.05

Option (D): reject Ho


Related Solutions

Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and...
Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and Population 2 does not. The data from these two samples is given below: Population 1: 71, 68, 67, 70, 70, 70, 67 Population 2: 69, 70, 73, 69, 76, 79, 75, 78 Is there evidence, at an α=0.02 level of significance, to conclude that there those who exercise regularly have lower resting heart rates? (Assume that the population variances are equal.) Carry out an...
Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and...
Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and Population 2 does not. The data from these two samples is given below: Population 1: 72, 71, 65, 65, 72, 73, 70 Population 2: 72, 72, 75, 70, 73, 69, 77, 77 Is there evidence, at an α=0.06 level of significance, to conclude that there those who exercise regularly have lower resting heart rates? (Assume that the population variances are equal.) Carry out an...
Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and...
Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and Population 2 does not. The data from these two samples is given below: Population 1: 64, 65, 63, 69, 70, 65, 68 Population 2: 69, 77, 73, 71, 79, 69, 70, 71 Is there evidence, at an α=0.001α=0.001 level of significance, to conclude that there those who exercise regularly have lower resting heart rates? (Use the conservative method for computing degrees of freedom). Carry...
Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and...
Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and Population 2 does not. The data from these two samples is given below: Population 1: 71, 63, 68, 71, 72, 66, 73 Population 2: 68, 78, 71, 68, 75, 69, 76, 72 Is there evidence, at an α=0.07 level of significance, to conclude that there those who exercise regularly have lower resting heart rates? Carry out an appropriate hypothesis test, filling in the information...
andom samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and...
andom samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and Population 2 does not. The data from these two samples is given below: Population 1: 68, 73, 71, 72, 64, 70, 68 Population 2: 74, 82, 81, 72, 76, 75, 75, 72 Is there evidence, at an α=0.05 level of significance, to conclude that there those who exercise regularly have lower resting heart rates? (Use the conservative method for computing degrees of freedom). Carry...
andom samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and...
andom samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and Population 2 does not. The data from these two samples is given below: Population 1: 68, 73, 71, 72, 64, 70, 68 Population 2: 74, 82, 81, 72, 76, 75, 75, 72 Is there evidence, at an α=0.05 level of significance, to conclude that there those who exercise regularly have lower resting heart rates? (Use the conservative method for computing degrees of freedom). Carry...
HW 30 #3 Random samples of resting heart rates are taken from two groups. Population 1...
HW 30 #3 Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and Population 2 does not. The data from these two samples is given below: Population 1: 71, 63, 65, 70, 71, 67, 70 Population 2: 73, 71, 78, 73, 73, 77, 70, 69 Is there evidence, at an α=0.06 α = 0.06 level of significance, to conclude that there those who exercise regularly have lower resting heart rates? Carry out an appropriate...
****MUST BE FAMILIAR WITH R STUDIO PROGRAMMING***** Random samples of resting heart rates are taken from...
****MUST BE FAMILIAR WITH R STUDIO PROGRAMMING***** Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and population 2 does not. The data from these two samples (in beats per minute) are given below: Exercise group (sample from population 1): 62.4, 64.1, 66.8, 60.7, 68.2, 69.2, 64.9, 70.9, 67.7, 68, 58.5, 58.9, 64.7 No exercise group (sample from population 2): 79.3, 73.8, 75.3, 74.7, 76.9, 74.9, 73.2, 75.7, 75.2, 76.7, 78.7 Estimate the difference...
Two random samples are taken, one from among UVA students and the other from...
Two random samples are taken, one from among UVA students and the other from among UNC students. Both groups are asked if academics are their top priority. A summary of the sample sizes and proportions of each group answering yes" are given below: UVA (Pop. 1): n1 = 89,\(\hat{p}_{1}\) = 0.81 UNC (Pop. 2): n2 = 86,\(\hat{p}_{2}\) = 0.561 Find a 97.3% confidence interval for the difference P1 – P2 of the population proportions. Confidence interval = _______ 
Consider the following results for two independent random samples taken from two populations. Sample 1 Sample...
Consider the following results for two independent random samples taken from two populations. Sample 1 Sample 2 n1 = 50 n2 = 30 x1 = 13.4 x2 = 11.7 σ1 = 2.3 σ2 = 3 What is the point estimate of the difference between the two population means? Provide a 90% confidence interval for the difference between the two population means (to 2 decimals). ( , ) Provide a 95% confidence interval for the difference between the two population means...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT