A medical researcher wanted to compare two different methods (A and B) for measuring cardiac output(L/min). Method A is the "gold standard" but is invasive (involves inserting a catheter into the main heartartery). Method B is less accurate but is non-invasive. To control for differences between persons, bothmethods are used on each person participating in the study. This allows measurements to be directlycompared for each method, per individual. Cardiac output for 18 subjects was measured by both methodsand some summary statistics of the data are summarized in the table below. Is there enough evidence toconclude that the cardiac output for method B is less than the cardiac output for method A on average at asignificance level of 0.025.Cardiac MethodAverageStandard deviationA185.71.59IB185.291.81Difference (d = A - B)180.410.65Perform a statistical test.(a) What are the null and alternative hypotheses?Но рHA P(b) What is the test statistic? (Round your answer to 3 decimal places, if needed.)(c) Using the statistical table, the p-value is 0.01 < p-value < 0.025 +(d) Based on the p-value, reject* the null hypothesis.(e) This data provides• sufficient evidence to conclude that the cardiac output for method B is,on average, less than• the cardiac output for method A.

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

Question

A medical researcher wanted to compare two different methods (A and B) for measuring cardiac output
(L/min). Method A is the "gold standard" but is invasive (involves inserting a catheter into the main heart
artery). Method B is less accurate but is non-invasive. To control for differences between persons, both
methods are used on each person participating in the study. This allows measurements to be directly
compared for each method, per individual. Cardiac output for 18 subjects was measured by both methods
and some summary statistics of the data are summarized in the table below. Is there enough evidence to
conclude that the cardiac output for method B is less than the cardiac output for method A on average at a
significance level of 0.025.
Cardiac Method
Average
Standard deviation
A
18
5.7
1.59
IB
18
5.29
1.81
Difference (d = A - B)
18
0.41
0.65
Perform a statistical test.
(a) What are the null and alternative hypotheses?
Но р
HA P
(b) What is the test statistic? (Round your answer to 3 decimal places, if needed.)
(c) Using the statistical table, the p-value is 0.01 < p-value < 0.025 +
(d) Based on the p-value, reject
* the null hypothesis.
(e) This data provides
• sufficient evidence to conclude that the cardiac output for method B is,
on average, less than
• the cardiac output for method A.

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