Past studies have indicated that the percentage of smokers was estimated to be about 35%. Given the new smoking cessation programs that have been implemented, you now believe that the percentage of smokers has reduced. You randomly surveyed 2376 people and found that 784 smoke. Use a 0.05 significance level to test the claim that the percentage of smokers has reduced.

a) Identify the null and alternative hypotheses?

H0H0: ? p = p ≠ p < p > p ≤ p ≥ μ = μ ≠ μ < μ > μ ≤ μ ≥  

H1H1: ? p = p ≠ p < p > p ≤ p ≥ μ = μ ≠ μ < μ > μ ≤ μ ≥  

b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)?

• left-tailed
• right-tailed
• two-tailed

c) Identify the appropriate significance level.


d) Calculate your test statistic. Write the result below, and be sure to round your final answer to two decimal places.


e) Calculate your p-value. Write the result below, and be sure to round your final answer to four decimal places.


f) Do you reject the null hypothesis?

• We reject the null hypothesis, since the p-value is less than the significance level.
• We reject the null hypothesis, since the p-value is not less than the significance level.
• We fail to reject the null hypothesis, since the p-value is less than the significance level.
• We fail to reject the null hypothesis, since the p-value is not less than the significance level.

• g) Select the statement below that best represents the conclusion that can be made.
• There is sufficient evidence to warrant rejection of the claim that the percentage of smokers is less than 35%.
• There is not sufficient evidence to warrant rejection of the claim that the percentage of smokers is less than 35%.
• The sample data support the claim that the percentage of smokers is less than 35%.
• There is not sufficient sample evidence to support the claim that the percentage of smokers is less than 35%

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

​

Verify that S_e ≈ 3.694, a ≈ 38.254, b ≈ 0.153, and , ∑x =447, ∑y =298, ∑x² =33,419, and ∑y² =14,858, and use a 5% level of significance to find the P-value for the test that claims that β is greater than zero.

Group of answer choices

A) Since the P-value is greater than α = 0.05, we reject the null hypothesis that the population slope β is equal to zero in favor of the alternate hypothesis that the population slope β is greater than zero.

B) Since the P-value is less than α = 0.05, we reject the null hypothesis that the population slope β is equal to zero in favor of the alternate hypothesis that the population slope β is greater than zero.

C) Since the P-value is equal to α = 0.05, we fail to reject the null hypothesis that the population slope β is equal to zero in favor of the alternate hypothesis that the population slope β is greater than zero.

D) Since the P-value is equal to α = 0.05, we reject the null hypothesis that the population slope β is equal to zero in favor of the alternate hypothesis that the population slope β is greater than zero.

E) Since the P-value is greater than α = 0.05, we fail to reject the null hypothesis that the population slope β is equal to zero in favor of the alternate hypothesis that the population slope β is greater than zero.

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information. x 61 67 75 86 73 73 y 40 39 48 51 44 51 (a) Verify that Σx = 435, Σy = 273, Σx2 = 31889, Σy2 = 12563, Σxy = 19974, and r ≈ 0.814. Σx Σy Σx2 Σy2 Σxy r (b) Use a 5% level of significance to test the claim that ρ > 0. (Use 2 decimal places.) t critical t Conclusion Reject the null hypothesis, there is sufficient evidence that ρ > 0. Reject the null hypothesis, there is insufficient evidence that ρ > 0. Fail to reject the null hypothesis, there is insufficient evidence that ρ > 0. Fail to reject the null hypothesis, there is sufficient evidence that ρ > 0. Correct: Your answer is correct. (c) Verify that Se ≈ 3.4562, a ≈ 8.064, b ≈ 0.5164, and x ≈ 72.500. Se a b x (d) Find the predicted percentage y hat of successful field goals for a player with x = 71% successful free throws. (Use 2 decimal places.) % (e) Find a 99% confidence interval for y when x = 71. (Use 1 decimal place.) lower limit % upper limit % (f) Use a 5% level of significance to test the claim that β > 0. (Use 2 decimal places.) t critical t

The Centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .28.

a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02 (rounded up to the next whole number)? Use 95% confidence. b. Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population (to 4 decimals)? c. What is the 95% confidence interval for the proportion of smokers in the population (to 4 decimals)?

Variable costs as a percentage of sales for Lemon Inc. are 80%, current sales are $600,000, and fixed costs are $130,000. What is the break even point in sales?

(a) You wish to estimate the mean percentage price change for all supermarkets in the Foodmart chain. From the sample of 150 stores, we have calculated the sample mean,

x = 4.092 and sample standard deviation, s = 0.795.
(i) Calculate the 99% confidence interval estimate of the mean percentage change

for all supermarkets in the Foodmart chain.

(ii) Provide a plain language interpretation of the interval you have just constructed.

(iii) Nationally, the Food component of the Australian CPI increased by 3.9% for the year to June 2008. From your earlier results, does it appear that food price changes at Foodmart are any different to those as a nation overall? Explain your reasoning.

Why are loans such a high percentage of total assets at the typical bank? What four broad classes of loans do banks engage in? Most non-financial firms would never hold as much of their assets in safe liquid securities as banks do. Why do banks maintain such a high percentage of investment in securities?

1f. Compare 1a and 1d, and 1b and 1e, explain why the percentage in 1a is much larger than that in 1d and why the value in 1b is much smaller than that in 1e?

1. Suppose that for Edwardsville High School, distances between students’ homes and the high school observe normal distribution with the average distance being 4.76 miles and the standard deviation being 1.74 miles. Express distances and z scores to two decimal places. Write the formula to be used before each calculation.

1a. What percentage of students in the high school live farther than 6.78 miles from the school?

1b. A survey shows that 8% of the students who live closest to the school choose to walk to school. What is the maximum walking distance of these 8% of students? In other words, what is the distance below which these 8% of students live from the school?

1c. Suppose that the school district’s policy allows students living beyond 4.50 miles from the school to take school buses to go to school. There are 3,567 students who enroll in the fall semester, 2006. How many students in the high school are not eligible to take school buses?

1d. Suppose all samples of size 12 are taken. What percentage of sample means has a value larger than 6.78 miles?

1e. Below what value are 8% of sample means of size 12?

A plant distills liquid air to produce oxygen, nitrogen and argon. the percentage of impurity in the oxygen is thought to be linearly related to the amount of impurities in the air as measured by the pollution count. in parts per million (ppm). A sample of plant operating data is show below. (a) state the hypothesis of a linear relationship between oxygen purity and input air purity and fit a linear regression model to the data. (b) Test significance of the regression. (c) Plot and analyze the residuals from the sample data and comment on model adequacy. Evaluate all three assumptions regrading the residuals. Explain how to do all of this using Minitab.

Count(ppm) Purity (%)

1.10 93.3
1.45 92.0
1.36 92.4
1.59 91.7
1.09 94.0
0.75 94.6
1.20 93.6
0.99 93.1
0.83 93.2
1.22 92.9
1.47 92.2
1.81 91.3
2.03 90.1
1.76 91.6
1.68 91.9