Question

During an angiogram, heart problems can be examined through a small tube threaded into the heart from a vein in the patient’s leg. It is important the tube is manufactured to have a diameter of 2.0mm. In a random sample of 12 tubes, the average was 2.025mm with a sample standard deviation of 0.021mm.

(a) Make a 99% confidence interval for the mean tube diameter. Conduct a Hypothesis test for mean tube diameter.

(b) What are the appropriate Null and Alternative Hypotheses

(c) Determine the appropriate reference distribution

(d) Calculate the test statistic

(e) Calculate the p-value

(f) What is your conclusion at the α = 0.01 significance level?

(g) What is your conclusion about the safety of the tubes being manufactured?

(h) Does the conclusion you reach from your hypothesis test agree with you answer in 3a? Explain

Answer 1

Answer:-

Given That:-

During an angiogram, heart problems can be examined through a small tube threaded into the heart from a vein in the patient’s leg. It is important the tube is manufactured to have a diameter of 2.0mm. In a random sample of 12 tubes, the average was 2.025mm with a sample standard deviation of 0.021mm.

(a) Make a 99% confidence interval for the mean tube diameter. Conduct a Hypothesis test for mean tube diameter.

given,

n = 12

s = 0.021

The 99% confidence interval is given by

(2.006, 2.044)

2.006 < < 2.044

(b) What are the appropriate Null and Alternative Hypotheses

The null hypothesis is

Against the alternative,

(c) Determine the appropriate reference distribution

This is a one - sample t - test

So, the appropriate distribution would be t - distribution.

(d) Calculate the test statistic

The test statistic is,  

  

= 4.1239

  

(e) Calculate the p-value

From t tables with df n-1 = 12 - 1 = 11, and

t = 4.124

We have p - value = 0.00168921  

p - value = 0.0017

(f) What is your conclusion at the α = 0.01 significance level?

Since,

p - value (= 0.0017) < (= 0.01)

We reject our null hypothesis, at = 0.01

(g) What is your conclusion about the safety of the tubes being manufactured?

The table which is manufactured have not a diameter of 2.00 mm

(h) Does the conclusion you reach from your hypothesis test agree with you answer in 3a? Explain

yes, the conclusion agrees with the answer 3A.

Since, = 2 does not belong to 2.006 < < 2.044

This interval, we reject our null hypothesis.

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