Question

Salary ($) |
Master's Degree (1 = Yes) |

61,500 | 0 |

69,200 | 0 |

76,000 | 0 |

78,700 | 0 |

81,500 | 0 |

83,800 | 0 |

84,200 | 0 |

84,300 | 0 |

85,400 | 1 |

87,200 | 0 |

88,700 | 0 |

90,700 | 1 |

97,200 | 0 |

97,600 | 1 |

99,900 | 1 |

100,000 | 1 |

101,800 | 1 |

102,700 | 1 |

103,400 | 0 |

111,300 | 1 |

Do NOT use the “finite population” corrections for standard deviation calculation in this problem. Just assume we’re dealing with an infinite population.

- Provide the formal null and alternative hypotheses for a hypothesis test of the question of whether or not the mean administrator salary is really $84,000.

Assume that the underlying population of administrator salaries is normally distributed.

- b.Conduct this hypothesis test based on the 95% significance level. What is the p-value? Do you reject or fail to reject your null hypothesis? Why?
- c. Create a 90% confidence interval for the mean administrator salary. Explain in a sentence, in layman’s terms, what this confidence interval implies.
- d. Compare your hypothesis test in part “b” to your confidence interval in part “c”. Do these results conflict with each other? (i.e., is it OK to find these two answers simultaneously?...if so, why?...OR, is there a conflict where it should be impossible for these results to occur simultaneously?)

Answer #1

We are 90% confident that the true mean administrator salary will
lie between $84391 and $94119, that is, there is a 90% chance of
the true mean administrator salary lying within this range.

(d) Yes, it is OK to conduct the hypothesis test and finding the
confidence interval. Here the hypothesis test and the confidence
interval are yielding the same results, that is, the true mean
administrator salary is not really $84000. It is more than
that.

Salary ($)
Master's Degree (1 = Yes)
61,500
0
69,200
0
76,000
0
78,700
0
81,500
0
83,800
0
84,200
0
84,300
0
85,400
1
87,200
0
88,700
0
90,700
1
97,200
0
97,600
1
99,900
1
100,000
1
101,800
1
102,700
1
103,400
0
111,300
1
a. The university system boasts
that over 60% of its administrators have master’s...

DATAfile: Administrator You may need to use the appropriate
technology to answer this question. Suppose the national mean
annual salary for a school administrator is $91,500 a year. A
school official took a sample of 25 school administrators in the
state of Ohio to learn about salaries in that state to see if they
differed from the national average. 77,600 76,000 90,700 97,200
90,700 101,800 78,700 81,300 84,200 97,600 77,500 75,700 89,400
84,300 78,700 84,600 87,700 103,400 83,800 101,300 94,700...

Salary ($)
Master's Degree (1 = Yes)
100000
1
76000
0
97200
1
90700
1
101800
1
88700
0
84200
0
97600
1
87200
0
84300
0
78700
0
102700
1
103400
0
83800
0
111300
1
81500
1
72200
0
85400
1
61500
0
99900
1
The university system boasts that over 70% of its
administrators have master’s degrees. Provide the formal null and
alternative hypotheses for a test of this question. Is this a one
or two-tailed hypothesis?...

1. Consider this hypothesis test:
H0: p1 - p2 = 0
Ha: p1 - p2 > 0
Here p1 is the population proportion of “yes” of
Population 1 and p2 is the population proportion of
“yes” of Population 2. Use the statistics data from a simple random
sample of each of the two populations to complete the following:
(8 points)
Population 1
Population 2
Sample Size (n)
400
600
Number of “yes”
300
426
Compute the test statistic z.
What...

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