## Math 115

1) In 2002, the mean age of an inmate on death row was 40.7 years. A

sociologist wants to test the claim that the mean age of a death-row

inmate has changed since then. She randomly selects 32 death-row

inmates and finds that their mean age is 38.9 with a sample standard

deviation of 9.6 years. Test the claim at the α = 0.05 level of significance.

**Claim:** µ ≠ 40.7

**H0: **µ = 40.7

** **

H1: µ ≠ 40.7

**Critical Value(s) = **± 2.040

** **

Test Statistic = 38.9− 40.7

** **

Fail to reject!

Conclusion:There is not sufficient sample evidence to support the claim that

the mean age is different from 40.7.

2) Nexium is a drug that can be used to reduce the acid produced by the

body and heal damage to the esophagus due to acid reflux. Suppose the

manufacturer claims that more than 94% of patients taking Nexium are

healed within 8 weeks. In clinical trials 213 of 224 patients were healed

after 8 weeks. Test the manufacturers claim at the α = 0.01 level of

significance.

**Claim:** P > 0.94

**H0: **P ≤ 0.94

** **

H1: P > 0.94

**Critical value(s) =** 2.33

** **

Test Statistic =
** **

Fail to Reject!

Conclusion:There is not sufficient sample evidence to support the claim that

more than 94% of patients are healed within 8 weeks.

3) A researcher claims that the mean height of women today is greater the

mean height of women in 1974 which was 63.7 inches. She obtains a simple

random sample of 45 women and finds the sample mean to be 63.9 inches.

Assume that the population standard deviation is 3.5 inches. Test the

researcher’s claim using a level of significance of α = 0.05.

**Claim:** µ > 63.7

** **

H0: µ ≤ 63.7

** **

H1: µ > 63.7

** **

Critical value(s) = 1.645

** **

Test Statistic =
** **

Fail to reject!

Conclusion: There is not sufficient sample evidence to support the claim that

the mean height today is greater than in 1994.

4) A drug company manufactures a 200-mg pain reliever. Specifications

demand that the standard deviation of the amount of the active

ingredient must not exceed 5 mg. You select a random sample of 30

tablets from a certain batch and find that the sample standard deviation

is 7.3 mg. Assume the amount of the active ingredient is normally

distributed. Test the claim that the standard deviation of the amount of

the active ingredient is greater than 5 mg using α = 0.05.

**Claim:** σ > 5

** **

H0: σ ≤ 5

** **

H1: σ > 5

** **

Critical value(s) = 42.557

**Test Statistic = **
** **

Reject Ho !

Conclusion: The sample data support the claim that σ > 5.

**Using this data set determine: **

i) the equation of the linear regression line (y = a + bx)

a = 6.55

y = 6.55 – 0.714x

ii) the correlation coefficient, r.

r = - 0.948

iii) Using α = 0.05, is there a linear correlation between x and y?

**Critical values = **± 0.811

Claim: ρ ≠ 0, so H0 : ρ = 0 & H1: ρ ≠ 0.

Test statistic is r = -0.948 which falls in the critical region so we

reject H0.

Yes, there is correlation between x & y.

** **

Source: http://www.math.utk.edu/~kbonee/115/exam3/115-Ex3s-F07.pdf

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