Researcher A is interested in finding out if the average income of elementary school teachers is different from the national average income for adults. According to recent census information, the average income for adults age 25 and older is $40,000.

1. (From Frankfort-Nachmias and Leon-Guerrero, 2002—same as problem 4 from Assignment 5.) Last week you constructed null and alternative hypotheses for the following three prompts.  This week you are asked to draw a conclusion based on the given hypothesis structure in each prompt, alpha, and Z meaning that I have already done step 1 (without assumptions), part (or all, depending upon how you choose your criteria-critical value or p to α comparison) of step 2, and all of step 3 for you in each prompt.  What can you conclude about the null hypothesis (reject or fail to reject H₀) and, in one sentence, what does this mean for the researcher’s hypothesis in each prompt?

1. 2 points Researcher A is interested in finding out if the average income of elementary school teachers is different from the national average income for adults. According to recent census information, the average income for adults age 25 and older is $40,000.
2. H₀:  µ = $40,000; H_a : µ ≠ $40,000.
3. α = .05
4. Z = 1.8

2. 2 points Researcher B believes that students in small liberal arts colleges attend more parties per month than students nationwide. Previous research has shown that nationally, undergraduate students attend an average of 2.5 parties per month.
3. H₀: µ < 2.5; H_a : µ > 2.5.
4. α = .05
5. Z = 1.8

50. 2 points Researcher C thinks that stress (measured on an “interval” scale from 1-100, 1 being very low and 100 being very high) will be lower for adults who own dogs (or other pets) than for the general adult population. The population mean (µ) of the general population is 50.
51. H₀:  µ > 50; H_a : µ < 50.
52. α = .05
53. Z = 1.8
54. 8 points. A researcher believes that donations to charity decline during times of economic hardship despite the heightened need. The researcher compares results from her sample to known population data about donations.  There are 625 respondents in the sample with a sample mean of $1260 in donations and a sample standard deviation (s) of $250.  The population mean (μ) is $1275 in donations with a population standard deviation (σ) of $200.  (All dollar values are adjusted for inflation.)  If the researcher uses α = .05, does the sample data provide support for the researcher’s hypothesis?  Remember to include all four steps of hypothesis testing.

 12 points. An economic sociologist is interested in studying how long in months it takes the average IT (information technology) firm to go from IPO (initial public offering) to turning a profit since the bursting of the technology bubble. Between 1990 and 1999, it was believed that it took IT firms 29.1 months to turn a profit, but there was no reliable data on a standard deviation. The sociologist draws a sample of firms that went public between 2000 and 2009 and found the following data (in months) regarding time between IPO and first turning a profit:  43; 28; 22; 34; 57; 40; 30; 33; 36; 54; 10; 20; 73; 24; 36; 20; 52.  Using α = .05, is it reasonable to conclude that his data will support the notion that it takes longer for IT firms to turn a profit in the first decade of the 21^st century than it did in the previous decade?

4. 8 points Suppose that years of education are normally distributed in the population of all registered voters age 25 and older in Michigan from the year 2000, with a mean (µ) of 14.72 and a standard deviation (σ) of 1.8. A political scientist believes that the education level of the electorate has changed in recent years and hopes to prove this by collecting data on years of education among a sample of 324 registered Michigan voters.  After collecting her data, she calculates the sample mean to be 14.91 years of education.  Can she conclude that the education level of the electorate has changed since 2000?  Perform this hypothesis test with α =.05.  Be sure to include all four steps for the hypothesis test.

5. 8 points. A national police organization is lobbying congress for funding to hire more police officers in cities nationwide. One of its arguments is that officers, on average, work significantly longer than full-time duty, assuming full-time is μ = 40 hours per week.  A random sample of n = 36 cities show a sample mean of 41.09 and a sample standard deviation of 2.725.  Using this data, conduct a hypothesis test at α = .01 and evaluate if this sample data supports the claim that officers are working more than 40 hours per week.

6. 8 points (From Frankfort-Nachmias and Leon-Guerrero, 2002) It is known that, nationally, doctors working for HMOs (health maintenance organizations) average 15.3 years (µ) of experience in their specialties, with a standard deviation of 7.2 years (σ).  The executive director of a well-respected HMO wants to initiate an advertising campaign emphasizing the experience of its doctors and wants to be 99% certain that its doctors are actually more experienced than the national HMO average.  A random sample of 144 doctors is drawn and the sample mean () is 16.5 years with a sample standard deviation (s) = 8.2.  Should the executive director authorize the ad campaign (does it seem likely that the HMO’s doctors are more experienced than the national average)?  Be sure to include all four steps for the hypothesis test.