Question

Please answer all of the questions

A consumer wanted to find out how accurate Siri (an Apple digital assistant) is, so he asked questions on general facts and recorded how many Siri got right. Out of the 299 questions, he asked Siri, Siri responded correctly to 132 of them. What is the estimate of the population proportion? What is the standard error of this estimate?

Question 1 options:

	1) The true population proportion is needed to calculate this.
	2) Estimate of proportion: 0.559, Standard error: 0.0017.
	3) Estimate of proportion: 0.441, Standard error: 0.0017.
	4) Estimate of proportion: 0.559, Standard error: 0.0287.
	5) Estimate of proportion: 0.441, Standard error: 0.0287.

Question 2 (1 point)

Historically, 72.98% of packages delivered by UPS are on time. Suppose 151 deliveries are randomly selected for quality control. What is the probability that less than 74.48% of the deliveries were on time?

Question 2 options:

	1) 0.3390
	2) 10.1284
	3) 0.5000
	4) >0.999
	5) 0.6610

Question 3 (1 point)

Fill in the blank. In a drive thru performance study, the average service time for McDonald's is 186.69 seconds with a standard deviation of 6.26 seconds. A random sample of 82 times is taken. There is a 43% chance that the average drive-thru service time is greater than ________ seconds.

Question 3 options:

	1) 185.59
	2) 186.81
	3) 187.79
	4) There is not enough information to determine this.
	5) 186.57

Question 4 (1 point)

Experimenters injected a growth hormone gene into thousands of carp eggs. Of the 234 carp that grew from these eggs, 34 incorporated the gene into their DNA (Science News, May 20, 1989). With a confidence of 90%, what is the margin of error for the proportion of all carp that would incorporate the gene into their DNA?

Question 4 options:

	1) 0.0230
	2) 0.0378
	3) 0.0009
	4) 0.0025
	5) 0.0295

Answer 1

Question 1

P = X / n = 132/299 = 0.4415

Standard Error = √( (p * q) / n) = 0.0287

5) Estimate of proportion: 0.441, Standard error: 0.0287.

Quesiton 2

Sampling distribution of p̂ is approximately normal if np >=10 and n (1-p) >= 10
n * p = 151 * 0.7298 = 110.1998
n * (1 - p ) = 151 * (1 - 0.7298) = 40.8002
Mean = = p = 0.7298
Standard deviation = = 0.036137

X ~ N ( µ = 0.7298 , σ = 0.036137 )
P ( X < 0.7448 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 0.7448 - 0.7298 ) / 0.036137
Z = 0.4151
P ( ( X - µ ) / σ ) < ( 0.7448 - 0.7298 ) / 0.036137 )
P ( X < 0.7448 ) = P ( Z < 0.4151 )
P ( X < 0.7448 ) = 0.6610

Question 3

X ~ N ( µ = 186.69 , σ = 6.26 )
P ( X > x ) = 1 - P ( X < x ) = 1 - 0.43 = 0.57
To find the value of x
Looking for the probability 0.57 in standard normal table to calculate Z score = 0.1764
Z = ( X - µ ) / σ
0.1764 = ( X - 186.69 ) / 6.26
X = 187.79
P ( X > 187.79 ) = 0.43

Question 4

Critical value   Z(α/2) = Z(0.1/2) = 1.645

Margin of Error = Z(α/2) √ ( (p*q) / n) = 0.0378