7.1 - 7.'3 Quiz

A burger manufacturer made 200 hamburger patties between 8am and 9am this morning. The machine that makes the

patties is supposed to produce patties so that their weight is approximately normally distributed with a mean of 8

ounces and a standard deviation of 0.54 ounces. An employee randomly selects 5 of the patties and finds that the

mean weight of the patties is 7.6 ounces. Identify the population, the parameter, the sample, and the statistic in the context of the burger manufacturer scenario.

• Population: 200 hamburger patties; Parameter: Mean weight of 200 patties; Sample: 5 patties; Statistic: Mean weight of 5 patties

• Population: 5 patties; Parameter: Mean weight of 5 patties; Sample: All hamburger patties; Statistic: Mean weight of all patties

• Population: All employees; Parameter: Mean weight of patties; Sample: 200 patties; Statistic: Mean weight of 200 patties

• Population: 200 patties; Parameter: Mean weight of 5 patties; Sample: All hamburger patties; Statistic: Mean weight of all patties

Would it be unusual to get a sample mean of 7.6 oz or less in a sample of size 5 from this population?

• Yes, because 7.6 oz is much lower than the population mean

• No, because 7.6 oz is within the expected range of variation

• Yes, because 7.6 oz is higher than the population mean

• No, because 7.6 oz is exactly the population mean

Here are the midterm exam scores for 4 students that meet with Mrs. Sharp for one-on-one tutoring.

Student A: 94 Student B: 82 Student C: 76 Student D: 68

(a) List all 6 possible SRSs of size n = 2, and calculate the mean midterm score for each sample.

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Here are the midterm exam scores for 4 students that meet with Mrs. Sharp for one-on-one tutoring.

Student A: 94 Student B: 82 Student C: 76 Student D: 68

.Which student has the highest midterm exam score?

• Student A

• Student B

• Student C

• Student D

About 10% of people in the United States do not wear a seat belt. Suppose we plan to select a random sample of 180 U.S. residents. Let p^ be the proportion of people in the sample who do not wear their seat belt. Calculate the mean of the sampling distribution of p^.

• 0.10

• 0.18

• 0.05

• 0.15

Calculate the standard deviation of the sampling distribution of p^ for a sample size of 180.About 10% of people in the United States do not wear a seat belt. Suppose we plan to select a random sample of 180 U.S. residents. Let p^ be the proportion of people in the sample who do not wear their seat belt.

• 0.022

• 0.030

• 0.015

• 0.045

What condition must be met for the sampling distribution of \( \hat{p} \) to be approximately normal?

• The sample size must be greater than 30.

• The sample size must be less than 50.

• The sample size must be large enough so that both \( np \) and \( n(1-p) \) are at least 10.

• The sample size must be exactly 100.

What is the probability that at least 15% of the individuals in the sample do not wear their seat belt?

• 0.013

• 0.10

• 0.15

• 0.20