A recent study found that 70% of all people over 60 years of age wear glasses. If a random sample of 8 people over 60 years of age was selected, find these probabilities: a) Exactly 4 people will wear glasses. b) At most 2 people will wear glasses. c) At least 2 people will wear glasses. Show work and use binomial probability table.

The rest of the questions on this lab activity (Questions 9-13) are multiple-choice. As you are answering each question, please explain your answers in addition to picking what you believe to be the correct letter choice.

9. Which of the following does not need to be known in order to determine the p-value?

A. the significance (or alpha) level

B. knowledge of whether the test is one-tailed (or one-sided) or two-tailed (or two-sided)

C. the value of the test statistic

D. All of the above need to be known to determine the p-value.

E. None of the above need to be known to determine a p-value.

10. You conduct a hypothesis test with a sample of size n = 40 and you observe values for the sample mean and sample standard deviation that do not lead to the rejection of the null hypothesis. In fact, you determine the p-value is 0.0667. What would you expect to happen to the p-value if the sample size was smaller? Assume here the sample mean and sample standard deviation would not change with the smaller sample size.

A. The p-value would stay the same

B. The p-value would increase (or get bigger)

C. The p-value would decrease (or get smaller)

D. This cannot be answered since p-values are not affected at all by sample size

11. If a p-value is smaller than the alpha level, what does this mean?

A. The results are practically important.

B. The null hypothesis does not provide a plausible explanation for the findings.

C. The null hypothesis is definitely false.

D. The alternative hypothesis is definitely true.

E. All of the above.

12. Which one of the following statements about p-values is correct?

A. If the p-value for a hypothesis test is 0.15, this means the probability that the null hypothesis is false is 0.15.

B. If a p-value is 0.04 and the alpha-level is 0.01, our decision should be to fail to reject the null hypothesis.

C. A p-value that is less than 0 means that we have an outcome that is extremely rare.

D. The smaller the p-value, the more evidence there is in favor of the null hypothesis.

E. All of the above statements are correct.   

13. Imagine you have data in the form of means, and you have conducted a hypothesis test. You obtain a p-value of 0.0001. Which of the following statements must be true regarding this p-value?

A. The difference between µ and must be huge.

B. Since the p-value is so small, the results will have practical importance as well as statistical significance.

C. The sample standard deviation, or s, must be very small.

D. All of the above.

E. None of the above.

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

It is estimated that 3.8% of the general population will live past their 90th birthday. In a graduating class of 728 high school seniors, find the following probabilities. (Round your answers to four decimal places.)

(a) 15 or more will live beyond their 90th birthday

(b) 30 or more will live beyond their 90th birthday

(c) between 25 and 35 will live beyond their 90th birthday

(d) more than 40 will live beyond their 90th birthday

From 77 of its restaurants, Noodles & Company managers collected data on per-person sales and the percent of sales due to "potstickers" (a popular food item). Both numerical variables failed tests for normality, so they tried a chi-square test. Each variable was converted into ordinal categories (low, medium, high) using cutoff points that produced roughly equal group sizes. At α = .01, is per-person spending independent of percent of sales from potstickers? Potsticker % of Sales Per Person Spending Low Medium High Row Total Low 11 4 8 23 Medium 6 11 6 23 High 4 13 14 31 Col Total 21 28 28 77 Click here for the Excel Data File

(a) The hypothesis for the given issue is H0: Percentage of Sales and Per-Person Spending are independent. No Yes

(b) Calculate the chi-square test statistic, degrees of freedom, and the p-value. (Round your test statistic value to 2 decimal places and p-value to 4 decimal places. Leave no cells blank - be certain to enter "0" wherever required.) Test statistic d.f. p-value

(c) We reject the null and find dependence. No Yes

In a four-digit lottery, each of the four digits is supposed to have the same probability of occurrence. The table shows the frequency of occurrence of each digit for 83 consecutive daily four-digit drawings. Digit Frequency 0 26 1 32 2 27 3 40 4 31 5 31 6 33 7 44 8 33 9 35 Total 332 Click here for the Excel Data File

(a) The hypothesis for the given issue is H0: The digits come from a uniform population. No Yes

(b) Calculate the chi-square test statistic, degrees of freedom, and the p-value. (Round your test statistic value to 2 decimal places and the p-value to 4 decimal places.) Test statistic d.f. p-value

(c) Find the critical value of the chi-square for α = .01. (Round your answer to 2 decimal places.) Critical value

(d) At α = .01, can you reject the hypothesis that the digits are from a uniform population? Yes No

Which of the following is not a characteristic of action research?

In 2017, the city of Burrusville contained 26,898 households. According to city records, 16,275 of these households had a dog. Use this information to answer the following questions.

a) What is p, the population proportion? Show your calculation and round your solution to three decimal places. (2 points)

b) Suppose a simple random sample of 140 homes were chosen at random, and 91 of these homes had a dog. Verify that the sampling distribution is approximately normal. (3 points)

c) What is the probability that a random sample of 140 homes from Burrusville would contain 91 or fewer with a dog? (4 points)

Comparing the standard deviation and variance equation. Analyze the statement of "once is never; twice is forever"

The average number of pounds of meat that a person consumes per year is 218.4 pounds. Assume that the standard deviation is 25 pounds and the distribution is approximately normal.

a) Find the probability that a person selected at random consumes less than 224 pounds of meat per year. Calculate the z-score manually, and use StatCrunch or the Standard Normal Table to calculate the probability, rounding to four decimal places. (4 points)

b) If a sample of 40 individuals were selected randomly, find the probability that the mean of the sample will be less than 224 pounds per year. Calculate the z-score manually, and use StatCrunch or the Standard Normal Table to calculate the probability, rounded to four decimal places. (4 points)

c) Why are the probabilities in parts (a) and (b) so different? (2 points)

During a study, individuals were asked to rate a product on a scale of 1-5. From the following data, help the researcher determine whether any significant differences exist in opinions among individuals from two different regions. (Note: Assume a significance level of 0.05 and assume that the population standard deviation is unknown). Show your work.

Question 1: Below is a dataset for a sample of 33 countries with indicators of Obesity Prevalence and GDP Per Capita for each country. How much variance in Obesity Prevalence is explained by GDP Per Capita? (Question pertains to Coefficient of Determination)

Question 2. Below is a crosstab table for the number of smokers among males and females in a sample of 100 people. Is there a statistically significant association between Gender and Smoking? (Use Chi-Square).

Last year, 46% of business owners gave a holiday gift to their employees. A survey of business owners indicated that 30% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 60 business owners.

4. A woman who smokers during pregnancy increase health risks to the infant so that it is known that about 20% (1/5) of female smokers quit smoking during pregnancy. Suppose that a random sample of 400 pregnant women who smoked prior to pregnancy contained 62 who quit smoking during pregnancy.
a. What is the point estimator for p, the population of female smokers who quit smoking during pregnancy?

b. What are the assumptions (requirements) for constructing a confidence interval for p?

c. Compute the 95 % confidence interval for p.

d. Find the margin of error from part c.

e. Interpret the confidence interval you found in part c.

f. Does the result from c) agree with the claim saying, “about 20% (1/5) of female smokers quit smoking during pregnancy”?

We are interested to see whether the level of the minimum wage affects employment. In order to study this issue they got data from a random sample of 330 California fast food restaurants before and after an increase in the Californian minimum wage from $3.30 to $4.10 per hour. The change in full time equivalent employees per restaurant in the sample before and after the increase was 0.8 with a variance of 77.5.

Test whether this suggests the increase in the minimum wage had an effect on employment.

Suppose we are doing a study on the proportion of people who have texted while driving. We will use a 90% confidence interval. We need to know what sample size to use before we do the study. What sample size should we use to guarantee that our MOE is 3% or smaller? Round your answer up to the nearest whole number. Group of answer choices 752

Question 2 Suppose we are doing a study on the proportion of people who have texted while driving. But this time we want to be more accurate, so we use a 99% confidence interval. We need to know what sample size to use before we do the study. What sample size should we use to guarantee that our MOE is 3% or smaller? Round your answer up to the nearest whole number. Note: Your answer should be much larger than the previous answer. Hypothesis Test Example For Proportions: What proportion of people do not drink alcohol? You believe that the proportion of people in the U.S.A. who do not drink is less than 15%. To determine if you are correct, you take a SRS of 400 U.S. residents, and find the proportion of people who do not drink in your sample is 0.22. Conduct a hypothesis test at the 5% significance level.

Question 3 Write the hypotheses for the test.

Question 4 Check the assumptions for the test. There are two assumptions you must test.

Question 5 What is the z-crit value? Round your answer to 2 decimal places. Include the correct sign.

Question 6 Calculate the value of the test statistic z-calc. Round your answer to 2 decimal places.

Question 7 Do you reject or fail to reject the null? Reject Ho Fail to Reject Ho

Question 8 Write the conclusion. State the significance level in the conclusion.

Question 9 Increasing sample size while holding the confidence level constant will increase the width of the confidence interval. True False

Question 10 Increasing the confidence level while holding the sample size constant will increase the width of a confidence interval. True False