$$p=0.43,\ q=0.57,\ p^{\wedge}=0.38,\ n=60,\ SE=0.0639$$ What is the probability that in a random sample of 60 drive-through customers, a majority $$\left(>50\%\right)$$ of them will have to wait more than 2 minutes? Use Desmos - Normal Distribution. Round your answer to four decimal places.

N(0.43, 0.0639) Min: 0.5 P(X > 0.5) = 0.1367

N(0.43, 0.0639) Max: 0.5 P(X > 0.5) = 0.8633

N(0, 1) Min: 0.5 P(X > 0.5) = 0.3085

N(0, 1) Max: 0.5 P(X > 0.5) = 0.6915

N(60, 0.38) Max: 0.5 P(X > 0.5) = 0

$$p=0.43,\ q=0.57,\ p^{\wedge}=0.38,\ n=60,\ SE=0.0639$$ At the 30th percentile, ____% of drive-through customers have to wait more than 2 minutes. Use Desmos - Normal. Convert your proportion to the nearest percent.

N(0.43, 0.0639) inverse(0.3) = 0.3964 = 40%

N(0.43, 0.0639) inverse(0.7) = 0.4635 = 46%

N(0, 1) inverse(0.7) = 0.5255 = 53%

N(0, 1) inverse(0.3) = -0.5244 = 52%

N(60, 0.38) inverse(0.3) = 59.80 = 60%

$$p=0.43,\ q=0.57,\ p^{\wedge}=0.38,\ n=60,\ SE=0.0639,\ z=-0.78$$ Does the Test Statistic (Z-Score) appear to indicate that it is unusual for 38% $$\left(p^{\wedge}=0.38\right)$$ of drive-through customers to have to wait more than 2 minutes?

No, a z-score of -0.78 indicates the point estimate $$\left(p^{\wedge}=0.38\right)$$ is not unusual because it is within 1 standard error or the mean.

Yes, since the z-score is negative, it indicates that the point estimate $$\left(p^{\wedge}=0.38\right)$$ is below the mean, which is unusual.

Yes, a z-score of -0.78 indicates the point estimate $$\left(p^{\wedge}=0.38\right)$$ is unusual because it beyond two standard errors of the mean.

No, a z-score of -0.78 indicates the point estimate $$\left(p^{\wedge}=0.38\right)$$ is not unusual because that is what the manager observed in the sample.

$$p=0.43,\ q=0.57,\ p^{\wedge}=0.38,\ n=60,\ SE=0.0639,\ z\ =-0.78$$ $$H_0:\ p=0.43,\ H_A:\ p $$P-Value\ =\ 0.2177,\ \alpha=0.05$$ Since the P-Value is higher than the allowed significance level, the manager's sample ___1___ provide convincing evidence that the true population proportion of drive-through customers who wait more than two minutes is less than 43%. Therefore, the manager should ___2___ the null hypothesis and conclude that the additional drive-through employee ___3___.

1) does not 2) fail to reject 3) did not improve customer wait times

1) does 2) fail to reject 3) improved customer wait times

1) does 2) reject 3) did not improve customer wait times

1) does not 2) reject 3) improved customer wait times

$$p=0.43,\ q=0.57,\ p^{\wedge}=0.38,\ n=60,\ SE=0.0639,\ z=-0.78$$ Construct a 95% Confidence Interval for the true population proportion of drive-through customers that have to wait more than 2 minutes. point estimate $$\pm$$ margin of error $$90\%\ CI:\ p^{\wedge}\pm1.65\times SE$$ $$95\%\ CI:\ p^{\wedge}\pm1.96\times SE$$ $$99\%\ CI:\ p^{\wedge}\pm2.58\times SE$$ We are 95% confident that the true population proportion of drive-through customers who have to wait more than 2 minutes is between

0.25 and 0.51 $$\Longrightarrow$$ 25% and 51%.

0.27 and 0.49 $$\Longrightarrow$$ 27% and 49%

0.22 and 0.54 $$\Longrightarrow$$ 22% and 54%

0.30 and 0.56 $$\Longrightarrow$$ 30% and 56%

Statistics Review 3 (Topics 8 - 10)

Authored by Jennifer Droemer

Mathematics

University

CCSS covered

Used 7+ times

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

The manager of a fast-food restaurant wants to reduce the proportion of drive-through customers who have to wait for more than 2 minutes to receive their food once their order is placed. Based on store records, 43% of all customers wait more than 2 minutes to receive their food. To try and reduce customer wait time, the manager hires an additional employee to assist with drive-through orders. After a month, the manager takes a random sample of 60 drive-through customers and finds that 23 of them have to wait more than 2 minutes to receive their food.
Parameter of Interest: The true population ________of drive-through customers who have to wait more than 2 minutes to receive their food.

mean

proportion

Tags

CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The manager of a fast-food restaurant wants to reduce the proportion of drive-through customers who have to wait for more than 2 minutes to receive their food once their order is placed. Based on store records, 43% of all customers wait more than 2 minutes to receive their food. To try and reduce customer wait time, the manager hires an additional employee to assist with drive-through orders. After a month, the manager takes a random sample of 60 drive-through customers and finds that 23 of them have to wait more than 2 minutes to receive their food.
p = probability of waiting more than 2 min. = _______

0.43

0.57

Tags

CCSS.HSS.IC.B.4

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The manager of a fast-food restaurant wants to reduce the proportion of drive-through customers who have to wait for more than 2 minutes to receive their food once their order is placed. Based on store records, 43% of all customers wait more than 2 minutes to receive their food. To try and reduce customer wait time, the manager hires an additional employee to assist with drive-through orders. After a month, the manager takes a random sample of 60 drive-through customers and finds that 23 of them have to wait more than 2 minutes to receive their food.
q = probability of waiting less than 2 min. = _______

0.43

0.57

Tags

CCSS.HSS.IC.B.4

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The manager of a fast-food restaurant wants to reduce the proportion of drive-through customers who have to wait for more than 2 minutes to receive their food once their order is placed. Based on store records, 43% of all customers wait more than 2 minutes to receive their food. To try and reduce customer wait time, the manager hires an additional employee to assist with drive-through orders. After a month, the manager takes a random sample of 60 drive-through customers and finds that 23 of them have to wait more than 2 minutes to receive their food.
n = sample size = _______

0.43

0.57

Tags

CCSS.6.SP.A.2

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The manager of a fast-food restaurant wants to reduce the proportion of drive-through customers who have to wait for more than 2 minutes to receive their food once their order is placed. Based on store records, 43% of all customers wait more than 2 minutes to receive their food. To try and reduce customer wait time, the manager hires an additional employee to assist with drive-through orders. After a month, the manager takes a random sample of 60 drive-through customers and finds that 23 of them have to wait more than 2 minutes to receive their food.
p^ = sample proportion = _______

0.43

0.57

Tags

CCSS.HSS.IC.B.4

MULTIPLE CHOICE QUESTION

1 min • 1 pt

MULTIPLE SELECT QUESTION

2 mins • 1 pt

Fail to reject the Null Hypothesis when the Alternative Hypothesis is true.

Deciding that wait times have NOT been significantly reduced, when they actually have.

Reject the Null Hypothesis when the Null Hypothesis is true.

Deciding that drive-through wait times have been significantly reduced but they have not.

Consequence: The restaurant continues to pay for an additional drive-through employee that they do not need.

Consequence: The restaurant gets rid of the extra drive-through employee, so wait-times increase again.

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