## Engage NY Eureka Math 7th Grade Module 5 End of Module Assessment Answer Key

### Eureka Math Grade 7 Module 5 End of Module Assessment Task Answer Key

Round all decimal answers to the nearest hundredth.

Question 1.

You and a friend decide to conduct a survey at your school to see whether students are in favor of a new dress code policy. Your friend stands at the school entrance and asks the opinions of the first 100 students who come to campus on Monday. You obtain a list of all the students at the school and randomly select 60 to survey.

a. Your friend finds 34% of his sample in favor of the new dress code policy, but you find only 16%. Which do you believe is more likely to be representative of the school population? Explain your choice.

b. Suppose 25% of the students at the school are in favor of the new dress code policy. Below is a dot plot of the proportion of students who favor the new dress code for each of 100 different random samples of 50 students at the school.

If you were to select a random sample of 50 students and ask them if they favor the new dress code, do you think that your sample proportion will be within 0.05 of the population proportion? Explain.

c. Suppose ten people each take a simple random sample of 100 students from the school and calculate the proportion in the sample who favors the new dress code. On the dot plot axis below, place 10 values that you think are most believable for the proportions you could obtain.

Explain your reasoning.

Answer:

a. My students were randomly selected instead of only the early arrivers. My students would be more representative.

b. A little more than half of these 100 samples are between 0.20 and 0.30, so there is a good chance, but a value like 0.10 should be even better.

c. The values will still center around 0.25 but will tend to be much closer together than in part (b) where samples only had 50 students. This is because a larger sample size should show less variability.

Question 2.

Students in a random sample of 57 students were asked to measure their handspans (the distance from the outside of the thumb to the outside of the little finger when the hand is stretched out as far as possible). The graphs below show the results for the males and females.

a. Based on these data, do you think there is a difference between the population mean handspan for males and the population mean handspan for females? Justify your answer.

b. The same students were asked to measure their heights, with the results shown below.

Are these height data more or less convincing of a difference in the population mean height than the handspan data are of a difference in the population mean handspan? Explain.

Answer:

a. Yes. The handspans tend to be larger for males. All but two males are at least 20 cm. Less than “50%” of the female handspans are that large. The number of MADs by which they differ is significant: \(\frac{21.6-19.6}{1}\) = 2.

b. They are even more convincing because there is less overlap between the two distributions. The number of MADs by which they differ is significant: \(\frac{70.5-64.1}{1.7}\) = 3.76.

Question 3.

A student purchases a bag of “mini” chocolate chip cookies and, after opening the bag, finds one cookie that does not contain any chocolate chips! The student then wonders how unlikely it is to randomly find a cookie with no chocolate chips for this brand.

a. Based on the bag of 30 cookies, estimate the probability of this company producing a cookie with no

chocolate chips.

b. Suppose the cookie company claims that 90% of all the cookies it produces contain chocolate chips. Explain how you could simulate randomly selecting 30 cookies (one bag) from such a population to determine how many of the sampled cookies do not contain chocolate chips. Explain the details of your method so it could be carried out by another person.

c. Now, explain how you could use simulation to estimate the probability of obtaining a bag of 30 cookies with exactly one cookie with no chocolate chips.

d. If 90% of the cookies made by this company contain chocolate chips, then the actual probability of obtaining a bag of 30 cookies with one chipless cookie equals 0.143. Based on this result, would you advise this student to complain to the company about finding one cookie with no chocolate chips in her bag of 30? Explain.

Answer:

a. \(\frac{1}{30}\) ≈ 0.0333

b. Have a bag of 100 counting chips; 90 of them are red to represent cookies containing chips, and 10 of them are blue to represent cookies without chips. Pull out a chip, record its color, and put it back. Do this “30” times, and count how many are not red.

c. Repeat the above process from part (b) many, many times (e.g., 1,000). See what proportion of these 1,000 bags had exactly one blue chip. That number over 1,000 is your estimate of the probability of a bag of 30 cookies with one chocolate chip.

d. No. That is not that small of a probability. I would not find the value convincing that this did not just happen to her randomly.