Problem 1: Hypothesis Testing (Adults saving for retirement)

in a recent conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement. Does the sample evidence suggest that a majority for adult Americans without a high school diploma are worried about having enough saved for retirement? Use a 0.05 level of significance.

1.state the null and alternative hypothesis?

2. What type of hypothesis test is to be used?

3. What distribution should be used and why?

4. is this a right, left, or two-tailed text?

5. Compute the test statistic?

6. Compute the p-value?

7. Do you reject or not reject the null hypothesis?explain why

8. What do you conclude?

Problem 2 (Google Stock)

Google became a publicly traded company in August 2004. Initially, the stock traded over 10 million shares each day! since the initial offering, the volume of stock traded daily has decreased substantially. in 2010, the mean daily volume in Google stock was 5.44 million shares, according to Yahoo! finance. A random sample of 35 trading days in 2014 resulted in a sample mean of 3.28 million shares with a standard deviation of 1.68 million shares. Does the evidence suggest that the volume of Google stock has changed since 2007? Use a 0.05 level of significance.

1. State the null and alternative hypothesis?

2. What type of hypothesis test is to be used?

3. What distribution should be used and why?

4. Is this a right, left, or two-tailed test?

5. Compute the test statistic?

6. Compute the p-value?

7. Do you reject or not reject the null hypothesis? Explain why?

8. What do you conclude

Problem 3 Confidence Interval (Healthcare for all Americans)

A Gallup poll found that 493 of 1050 adult Americans believe it is the responsibility of the federal government to make sure all Americans have Healthcare Coverage.

1. What is the sample in this study? what is the population of interest?

2. What is the variable of interest in this study? is it qualitative or quantitative?

3. Based on the result of this study, obtain a point estimate for the proportion of adult Americans who believe it is responsibility of the federal government to make sure all Americans have healthcare coverage?

4. Explain why the point estimate in #3 is a statistic? what is it random variable?

5. Construct and interpret a 90% confidence interval for the proportion of adult Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage

6. Name two things that might be done to increase the precision of the confidence interval?

Problem 4 Speeding in a construction zone

A group of Brigham Young University-Idaho students collected data on the speed of vehicles traveling through a construction zone on a state highway, where the speed was 25 mph. The recorded speed (in mph) of 14 randomly selected vehicles is given below.

20,24,27,28,29,30,32,33,34,36,38,39,40,40

1. Assuming speeds are approximately normally distributing, construct 95% confidence interval for the true mean speed of drivers in this construction zone.Interpret the interval

2. Construct a 99% confidence interval for the true mean speed of drivers in this construction zone. Interpret the interval

3. Compare in this widths of the 95% and 99% confidence intervals?

4. What conclusions do you draw about the speed people drive in this construction zone?

Problem 5 Normal Probability Distribution

The Graduate Record Examination (GRE) is a test required for admission to may U.S. graduate school. Students' scores on the quantitative portion of the GRE follow a normal distribution with mean 150 and standard deviation 8.8. A graduate school requires that students score above 160 to be admitted.

1. What proportion of combined GRE scores can be expected to be over 160?

2. What proportion of combined GRE scores can be expected to be under 160?

3. What proportion of combined GRE scores can be expected to be between 155 and 160?

4. What is the probability that a randomly selected student will score over 145 point?

5. What is the probability that a randomly selected student will score less than 150 point?

6. What is the percentile rank of a student who earn a quantitative GRE score of 142?

7. Historically, Depart of History at NYU has admitted students whose quantitative GRE score is at least at the 61st percentile. What is the lowest GRE score of the student they admit?

8. Determine the 80th percentile of combined GRE scores?

9. Determine the combined GRE scores that make up the middle 95% of all scores

Use the standard normal distribution to determine the following

68% of the scores lie between what two values?

95% of the score lie between what two values?

99% of the scores lie between what two values