A simple random sample of pulse rates of

Avery Velasquez

Avery Velasquez

Answered question

2022-03-17

A simple random sample of pulse rates of 25 women from a normally distributed population results in a standard deviation of 12.7 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pullse rates of women have a standard deviation equal to 10 beats per minute. Complete parts (a) through (d) below.
a. Identify the null and alternative hypotheses. Choose the correct answer below.
A. H0:σ10 beats per minute, H1:σ=10 beats per minute
B. H0:σ=10 beats per minute, H1:σ10 beats per minuteSNKC. H0:σ=10 beats per minute, H1:σ<10 beats per minute
D. H0:σ10 beats per minute, H1:σ<10 beats per minute
b. Compute the test statistic.
χ2=
(Round to three decimal places as needed.)
c. Find the P-value of the test statistic.
The P-value of the test statistic is 
(Round to three decimal places as needed.)
d. State the conclusion.
'Reject'/'Fail to reject' H0 'is'/'is not' sufficiert evidence to warrant rejection of the claim that pulse rates of women have a standard deviation equal to 10 beats per minute.

Answer & Explanation

Tavolillaqra

Tavolillaqra

Beginner2022-03-18Added 4 answers

a). The null hypothesis states that population standard deviation is equal to 10.
The alternative hypothesis states that population standard deviation is not equal to 10.
Thus, the correct option is:
b). H0:σ=10 beats per minute, H1:σ10 beats per minute
b). The formula of chi-square test statistic is:
χ2=(n1)s2σ2
Given:
n=25
σ=10
s=12.7
The calculation for chi-square test statistic is as follows:
χ2=(251)12.72102=3870.96100=38.709
Thus, the value of chi-square test statistic is 38.709.
c). The degree of freedom is as follows:
df=n-1=25-1=24
Observe df=24 in the chi-square table to obtain the p-value. The answer is 0.029.
Thus, p-value =0.029
massifyc9

massifyc9

Beginner2022-03-19Added 3 answers

d). Level of significance=0.10
If the p-value is less than the significance level, we Reject the null hypothesis.
As 0.029<0.10, we REJECT the null hypothesis. Hence we have sufficient evidence to reject the null hypothesis.
Thus, the correct options are:
1. Reject;
2. Is

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