Algebra 2 | Unit 7: Statistical Inferences | End-of-Unit Assessment

• Candidate A will win because the mean percentage for the poll is greater than 50%.

• Candidate A cannot get more than 58% of the vote.

• The poll predicts that between 48.1% and 57.9% of voters will select candidate A in the election.

• The poll should not be trusted since it has a margin of error attached to it.

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HSS-IC.B.4

In the 1940s, the U.S. Department of Commerce reported a new way to test the tensile strength, in pounds per square inch, of concrete. Several samples of concrete specimens were used to estimate the mean tensile strength of 430 pounds per square inch with a margin of error of 10 pounds per square inch. After the study was published, another group proposes to run the same test on concrete specimens but with samples including many more concrete specimens in each sample. Which of these statements is most likely to be true about the second study?

• The estimated mean will be greater than 440 pounds per square inch.

• The margin of error for the second study will likely be around 10 pounds per square inch.

• The margin of error for the second study will likely be greater than 10 pounds per square inch.

• The margin of error for the second study will likely be less than 10 pounds per square inch.

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HSS-IC.B.4

Forty volunteer drivers are separated into two groups of 20 drivers each at random. The first group is asked to pay particular attention to braking smoothly when approaching a red light or stop sign. The second group is given no special instructions. All drivers report, at the end of a month, the gallons of gasoline used. The mean for the first group is 43.16 gallons of gas. The mean for the second group is 54.63 gallons of gas. The difference in means for the two groups is -11.47 gallons of gas. The data for both groups are combined and redistributed at random into two groups of 20. The means for each redistributed group are calculated, and the difference in means is recorded. The differences are represented in the histogram. Which of these conclusions and justifications is the most reasonable?

• The difference in means for the two treatment groups is likely due to the random assignment since the difference is negative.

• The difference in means for the two treatment groups is likely due to the random assignment since there is at least one value in the histogram with a greater absolute difference than 11.47 gallons of gas.

• The randomization distribution does not give any evidence that the difference between the two treatment groups is due to the special instructions.

• The randomization distribution provides strong evidence that the difference in means for the two treatment groups is due to the treatment because the difference is highly unlikely based on random assignment alone.

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HSS-IC.B.5

A student measures the wingspans of 40 local dragonfly specimens selected at random. The sample mean is 6.8 centimeters with a margin of error of 0.9 centimeters. Based on this information, what are plausible values for the mean wingspans of the population of local dragonflies?

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HSS-IC.B.4

The reaction times are measured for 50 college students who are randomly assigned to two groups. The students in group 1 listen to loud music during the test and the students in group 2 perform the test in silence. There are 25 students in each group.

The mean for the loud-music group is 2.64 seconds, and the mean for the silent group is 3.22 seconds. The data for both groups is combined, 25 reaction times are selected at random, and the mean of these reaction times is compared to the mean of the remaining 25 reaction times. This process is repeated 14 times. The means for the groups are summarized in the table.

mean of group 1	mean of group 2	difference in means
2.73	3.13	-0.40
2.99	2.87	0.12
2.60	3.26	-0.66
2.81	3.05	-0.24
3.10	2.76	0.34
3.24	2.62	0.62
3.22	2.64	0.58
2.63	3.23	-0.60
2.52	3.34	-0.82
2.91	2.95	-0.04
3.06	2.80	0.26
3.31	2.55	0.76
3.41	2.45	0.96
2.51	3.35	-0.84

Is the difference in the mean reaction times from the original experimental groups likely due to chance, or is there evidence that the music has an effect on reaction time? Explain your reasoning.

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HSS-IC.B.5

A scientist is worried about a new disease being spread by mosquitoes in an area. The scientist captures a random sample of 137 mosquitoes from the area and tests them to find out whether they carry the disease. In this sample, 22 of the mosquitoes were carrying the disease. Using this information, the scientist uses 100 simulations of additional samples with the same proportion of disease-carrying mosquitoes from the sample to determine that the standard deviation for the proportion of mosquitoes carrying the disease is approximately 0.029. 1. Estimate the proportion of mosquitoes in the area that carry the disease, and provide a margin of error. Explain or show your reasoning. 2. Why did the scientist run the simulations to find additional possible proportions of mosquitoes in the area that carry the disease?

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HSS-IC.B.4

A cell phone company selects 12 different stores in similar markets to advertise a new phone. Seven of these are randomly chosen to use an interactive digital display, and 5 other stores are randomly chosen to use a cardboard display. The company wants to know if the stores with the interactive digital displays are selling more phones than the stores with the cardboard displays. The table shows the number of the new phones sold at each of the stores during one week.

interactive digital display	cardboard display
12	11
23	30
18	17
26	10
9	16
15
28

1. Find the difference in mean number of new phones sold at the stores using the interactive display and stores using the cardboard display. Explain or show your reasoning. 2. An analyst combines the data in one group, then redistributes the data using a random process into a group of 7 and a group of 5. The analyst finds the mean for each group and records the difference. The process is repeated many times. A dot plot showing the differences in means for the randomized groupings is created. What conclusions, if any, can you draw about the new phone sales based on display type? Explain your reasoning. 3. After looking back at the data, the store manager for the store with a cardboard display that sold 30 of the new phones realizes there was a mistake—the store really only sold 3 of the new phones, not 30. What conclusions, if any, can you draw about the new phone sales based on display type using the corrected randomization distribution? Explain your reasoning.

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HSS-IC.B.5