Question

**Use this information to answer the following 6
questions:**

A study is being conducted to compare the average training time for two groups of airport security personnel: those who work for the federal government and those employed by private security companies. From a random sample of 12 government-employed security personnel, average training time was 72 hours, with a sample standard deviation of 8 hours. In a random sample of 16 privately employed security personnel, training time was 65.4 hours, with a sample standard deviation of 12.3 hours. Assume that training time for each group is normally distributed. Use the following notations:

μ_{1}: The mean training time for the population of
airport security personnel

employed by the federal government.

μ_{2}: The mean training time for the population of
airport security personnel

employed by private security companies.

The goal of the statistical analysis is to determine whether the sample data support the hypothesis that average training time for government-employed security personnel is higher than those employed by private security companies.

1)

What is the null hypothesis H(0)?

Select one:

a. μ1- μ2 ≥ 0

b. μ1- μ2 = 0

c. μ1- μ2 ≤ 0

d. μ1- μ2 < 0

2)

What is the alternative hypothesis H(a)?

Select one:

a. μ1- μ2 = 0

b. μ1- μ2 ≥ 0

c. μ1- μ2 ≤ 0

d. μ1- μ2 > 0

3)

What is the standard error of Xbar 1 Xbar 2?

Select one:

a. 2.83

b. 10.15

c. 3.85

d. 5.29

4)

What is the value of the test statistic?

Select one:

a. 1.72

b. 1.35

c. 1.22

d. 0.65

5)

What is the p-value?

Select one:

a. 0.99

b. 0.01

c. 0.12

d. 0.049

6)

At α=0.1 and using the p-value

Select one:

a. We reject H(0) in favor of H(a)

b. We do not reject H(0)

Answer #1

1)c. μ1- μ2 ≤ 0

2)

d. μ1- μ2 > 0

3)

x_{1}
= |
72.000 |
x_{2}
= |
65.400 |

s_{1}
= |
8.000 |
s_{2}
= |
12.300 |

n_{1}
= |
12.000 |
n_{2}
= |
16.000 |

standard error
se=√(S^{2}_{1}/n_{1}+S^{2}_{2}/n_{2})= |
3.85 |

4)

test stat t =(x_{1}-x_{2}-Δ_{o})/Se= |
1.72 |

5)

p value =0.049

d. 0.049

6)

a. We reject H(0) in favor of H(a) (since p value <0.05)

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