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# Question 1: In a large city, 46% of adults support the local football team building a...

Question 1: In a large city, 46% of adults support the local football team building a new stadium. If a poll is taken from a random sample of 80 adults in the large city, which of the following properly describes the sampling distribution of the sample proportion of adults who support the stadium?

A) Mean: 36.8, Sigma P-hat: 4.46, the distribution is approximately normal.

B) Mean: 36.8, Sigma P-hat: 4.46, shape of the distribution is unknown.

C) Mean: 0.46, Sigma P-hat: 0.056, the distribution is approximately normal.

D) Mean: 0.46, Sigma P-hat: 0.056, shape of the distribution is unknown.

E) Mean: 43.2, Sigma P-hat: 4.46, the distribution is binomial.

Question 2: Which of the following statements is true?

A) A parameter is a number that describes some characteristic of a sample.

B) An unbiased estimator is any statistic that is taken from a sample chosen by random methods.

C) A sampling distribution is the distribution of a statistic calculated from all possible samples of the same size from the same population.

D) The variability of a population distribution will decrease as the sample size increases.

E) A normal approximation can always be used for the sampling distribution of P-hat as long as the sample size is greater than 30

Question 3: The weight of a single bag checked by an airplane passenger follows a distribution that is right skewed with a mean of 38 pounds and a standard deviation of 6.2 pounds. If a random sample of 96 bags is selected, what is the probability that the average weight of the bags exceeds 40 pounds?

A) 0.0008

B) 0.0011

C) 0.3735

D) 0.9992

E) It is not appropriate to use a normal distribution to calculate probability in this situation.

1)

 np= 36.8 n(1-p)= 43.2
 here population proportion=     p= 0.4600 sample size       =n= 80 std error of proportion=σp=√(p*(1-p)/n)= 0.056

C) Mean: 0.46, Sigma P-hat: 0.056, the distribution is approximately normal.

2)

C) A sampling distribution is the distribution of a statistic calculated from all possible samples of the same size from the same population.

3)

 for normal distribution z score =(X-μ)/σ here mean=       μ= 38 std deviation   =σ= 6.2000 sample size       =n= 96 std error=σx̅=σ/√n= 0.6328
 probability =P(X>40)=P(Z>(40-38)/0.633)=P(Z>3.16)=1-P(Z<3.16)=1-0.9992=0.00080

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