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12) Why do we have a margin of error in statistics? If statistics are meant to be accurate, why are they sometimes accompanied by an estimate of doubt?

Discuss the concept of Margin of error as it relates to sample size.

Find at least examples of 3 studies or reports online that used a margin of error to draw conclusions or make a prediction. Respond to at least two other post

11)

After completing *Assignment* 4 (Module 6) located in Confidence Interval for Means Page on Canvas, discuss:

( a) The differences between the Z- interval and T- interval.

(b) What determines when to use Z interval and T interval

(c ) Which interval would be appropriate to use for the project? Justify your answer.

Module 7 )

1. An industrial company claims that the mean pH level of the water in a nearby river is 6.8. You randomly select 19 water samples and measure the pH of each. The sample mean and standard deviation are 6.7 and 0.24,respectively. Is there enough evidence to reject the company’s claim at ? = 0.05? Assume the population is normally distributed .

2. Susan goes to her doctor because she thinks she is ill.

(a) What is H0, Ha?

(b) Type I error? Type II error?

(c) Which of the errors are more serious and why?

Module 6 )

Q 1.

According to a Boston Globe story, only about 1 in 6 Americans have blue eyes, whereas in 1900 about half had blue eyes. (Source:Data from The Boston Globe October 17, 2006.)

a. For a random sample of 100 living Americans, find the mean and standard deviation of the proportion that have blue eyes.

b. In a *course* you are taking with 100 *students*, half of the *students* have blue eyes. Would this have been a surprising result if the sample were a random sample of Americans? Answer by finding how many standard deviations that sample result falls from the mean of the sampling distribution of the proportion of 100 *students* who have blue eyes.

c. In part b, identify the population distribution, the data distribution, and the sampling distribution of the sample proportion.

Q 2.

An *exam* consists of 50 multiple-choice questions. Based on how much you studied, for any given question you think you have a probability of p=0.70 of getting the correct answer. Consider the sampling distribution of the sample proportion of the 50 questions on which you get the correct answer.

a. Find the mean and standard deviation of the sampling distribution of this proportion.

b.What do you expect for the shape of the sampling distribution? Why?

c. If truly p=0.70, would it be very surprising if you got correct answers on only 60% of the questions? Justify your answer by using the normal distribution to approximate the probability of a sample proportion of 0.60 or less.