1 - Colorado Mesa University



HW #9 – HT and CI for Independent Means

Note that for each problem parts C through G are:

C) Give the critical value(s) (from the table).

D) Give the value of the test statistic (from the data).

E) Is the answer Yes or No?

F) What is the p-value?

G) Describe the meaning of the p-value in everyday terms.

Also all sample data are given at the end of the assignment.

1. (IN CLASS) Can we prove that City A and City B differ as far as the average age of their residents? Assume SRS’s.

A) What is the chance that we will conclude a difference when there is none?

B) What is the chance that we won’t conclude a difference when there is?

H) Give a 95% CI for the mean difference (City B – City A) for all residents.

2. (ANSWER GIVEN) Can we prove that City B and City C differ as far as the average age of their residents? Use the 1% significance level and assume SRS’s.

A) What is the chance that we will conclude a difference when there is none?

B) What is the chance that we won’t conclude a difference when there is?

H) Give a 95% CI for the mean difference (City B – City C) for all residents.

3. (SOLUTION GIVEN) Can we prove that Corn A on average matures sooner than Corn B? Assume acres were divided up randomly between the types and use the 5% significance level.

A) What is the chance that we will conclude Corn B matures sooner on average when it doesn’t?

B) What is the chance that we won’t conclude Corn B matures sooner on average when it actually does?

H) Give a 95% CI for the mean difference (Corn B – Corn A) for the population.

4. (HOMEWORK) Can we prove that Corn A has a higher yield on average than Corn B? Assume acres were divided up randomly between the types and use the 10% significance level.

A) What is the chance that we will conclude Corn A has a higher yield on average when it doesn’t?

B) What is the chance that we won’t conclude Corn A has a higher yield on average when it actually does?

H) Give a 95% CI for the mean difference (Corn A – Corn B) for the population.

5. (ALTERNATIVE HW) Can we prove that Corn A has a higher yield on average than Corn C? Assume acres were divided up randomly between the types and use the 5% significance level.

A) What is the chance that we will conclude Corn A has a higher yield on average when it doesn’t?

B) What is the chance that we won’t conclude Corn A has a higher yield on average when it actually does?

H) Give a 95% CI for the mean difference (Corn A – Corn C) for the population.

6. (IN CLASS) Can we prove that Bee Species X has a higher wing stroke frequency on average as compared to Bee Species Y? Assume SRS’s from normal populations.

A) What is the chance that we won’t conclude Bee Species X has a higher wing stroke frequency on average when it actually does?

B) What is the chance that we will conclude Bee Species X has a higher wing stroke frequency on average when it doesn’t?

H) Give a 95% CI for the mean difference (Bee Species X – Bee Species Y) for the populations.

7. (ANSWER GIVEN) Can we prove that Bee Species Y has a lower wing stroke frequency on average as compared to Bee Species Z? Assume SRS’s from normal populations and use the 5% significance level.

A) What is the chance that we won’t conclude Bee Species Y has a lower wing stroke frequency on average when it actually does?

B) What is the chance that we will conclude Bee Species Y has a lower wing stroke frequency on average when it doesn’t?

H) Give a 95% CI for the mean difference (Bee Species Z – Bee Species Y) for the populations.

8. (SOLUTION GIVEN) Can we prove that the “Right-Eye” method is any different than the “Left-Eye” method for mean shooting accuracy for beginning shooters? Assume beginning shooters were divided up randomly and the populations of shooting scores are normal. Use the 5% significance level.

A) What is the chance that we won’t conclude a difference when there actually is?

B) What is the chance that we will conclude a difference by mistake?

H) Give a 95% CI for the mean difference (Left – Right) for the populations.

9. (HOMEWORK) Can we prove that the “Both-Eye” method is any different than the “Left-Eye” method for mean shooting accuracy for beginning shooters? Assume beginning shooters were divided up randomly and the populations of shooting scores are normal. Use the 1% significance level.

A) What is the chance that we won’t conclude a difference when there actually is?

B) What is the chance that we will conclude a difference by mistake?

H) Give a 95% CI for the mean difference (Both – Left) for the populations.

10. (ALTERNATE HW) Can we prove that the “Both-Eye” method is any different than the “Right-Eye” method for mean shooting accuracy for beginning shooters? Assume beginning shooters were divided up randomly and the populations of shooting scores are normal. Use the 10% significance level.

A) What is the chance that we won’t conclude a difference when there actually is?

B) What is the chance that we will conclude a difference by mistake?

H) Give a 95% CI for the mean difference (Both - Right) for the populations.

DATA:

1, 2.

| |City A |City B |City C |

|Sample size |77 |81 |51 |

|Sample mean age |37.5 |42.6 |40.0 |

|Sample standard deviation |17.8 |13.2 |15.1 |

3.

| |Corn A |Corn B |

|Sample size |51 |122 |

|Sample mean maturity time |121 days |126 days |

|Sample standard deviation |10 |8 |

4, 5.

| |Corn A |Corn B |Corn C |

|Sample size |41 |123 |29 |

|Sample mean yield bushels per acre |531 |521 |511 |

|Sample standard deviation |55 |44 |33 |

6, 7.

| |Species X |Species Y |Species Z |

|Wing stroke frequencies |235, 225, 190, 192 |180, 169, 180, 184, 175, 183 |180, 177, 179, 184, 189, 189, 194, 179 |

8, 9, 10.

| |Right |Left |Both |

|Shooting accuracy scores after training |14,12,20,14,16 |12,19,18,15 |18,16,18,13,22,23 |

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