AP Statistics

Test of Significance for Proportions

1.  Gregor Mendel, an Austrian monk, proposal the genetic theory of inheritance in 1866. He supported his theory with the results of 8 years of experiments breeding peas and examining the inheritance of seven different characteristics. One characteristic studied was plant height. Mendel crossed purebred tall plants with purebred short plants. He proposed that when he bred these hybrids, one-quarter of their progeny would be pure short. Mendel reported that out of 1,064 randomly selected plants, 277 were short. Does he have the evidence to support his theory?

2.  A new radar device is being considered for a certain defense missile system. The system is checked by experimenting with actual aircraft in which a kill or a no kill is randomly simulated. The claim of the current company states that the probability of a kill with the new system does not exceed the 0.8 probability of the existing device. If in 300 trials with the new radar device there were 250 kills, does the current company’s claim have merit? Use a = .01.

3.  Artists often submit pictures of their work to be reviewed by judges who then decide which artists’ work will be selected for an exhibition. In the 1980 Marietta College Crafts National Exhibition, a total of 1,099 artists applied to be included in a national exhibit of modern crafts while only 216 were selected to send their crafts. Although Marietta College claims tries to take 25% of the work submitted, test the claim that in the 1980 exhibit the percent was smaller.

4.  A die is tossed 180 times. The resulting tallies show that thirty six times a “3” was displayed. Is this a balanced die?

5.  Is Elvis alive? USA Today ran a report about a University of North Carolina poll of a random sample of 1248 adults from the southern United States. It was reported that 8% of those surveyed believe that Elvis Presley still lives. The article began with the claim that “almost 1 out of 10” Southerners still thinks Elvis is alive. At the 0.01 significance level, test the claim that the true percentage is less than 10%.

6.  A pen company that made bold claim about how long their pens lasted recently had their pens tested by a consumer advocacy group. The results of a random sample of the test results are listed below:

161.9 166.4 168.0 168.9 171.4 171.9 172.1 172.8 173.6 174.7 177.4 178.14

179.7 181.8 182.0 182.1 184.9 186.8 187.6 189.9 190.4 191.3 192.1 193.0

193.2 192.9 193.9 194.8 195.7 196.2 196.4 198.5 199.7 200.4 204.2 205.1

206.9 210.4 212.2 212.9

  1. The research group stated that the pen company pens last on average 185 hours. The pen company claims the pens last longer. Does the evidence support the pen company (a = .02)?
  2. Another pen company spokesmen admitted off the record that he believes at least 50% of their pens will last longer than 180 hours. Is this claim justified (a = .02)?

#1

A city counsel is trying to decide to levy an additional gas tax to help with city improvements. A random sample of 400 voters in the city are asked if they favor an additional 4% gasoline sales tax to provide badly needed revenues for street repairs. The counsel has decided it will implement the tax if at least 60% of the voters favor the tax. The survey finds 220 out of the 400 favor the tax. Should the counsel proceed?

#2

Ten engineering schools in the U.S. were surveyed. The random sample contained 175 chemical engineers. Of these students, 40 were female. Compute a 90% confidence interval for the true proportion of chemical engineering student who were female.

#3

A study was done to determine if 12-15 year old girls who want to be engineers differ in IQ from the average of all girls. The mean IQ of all girls in this age range is known to be about 100. A random sample of 49 girls is selected, who state that they want to be engineers and their IQ is measures. The mean IQ of the girls in the sample is 104.5 with a standard deviation of 14.4. Does this finding provide evidence, at the 0.05 level of significance, that the mean IQ of 12 – 15 year old girls who want to be engineers differs from the average?

#4

At a certain college it is estimated that at most 25% of the students ride bicycles to class. Does this seem to be a valid estimate if, in a random sample of 90 college students, 28 are found to ride bicycles to class?

#5

The average math SAT score at Hammerhead High School over the years is 520. The mathematics faculty believes that this year’s class of seniors is the best the school has ever had in mathematics. One hundred seventy-five seniors take the exam and achieve an average score of 531 with a standard deviation of 96. Does this performance provide good evidence that this year’s class of fighting sharks is higher than average?