Suppose that LMN stock currently is selling at $79 per share. You buy 500 shares using $30,000 of your own money, borrowing the remainder of the purchase price from your broker. The rate on the margin loan is 5%.

a. What is the percentage increase in the net worth of your brokerage account if the price of LMN immediately changes to: (i) $87.20; (ii) $79; (iii) $70.80? What is the relationship between your percentage return and the percentage change in the price of LMN? (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

b. If the maintenance margin is 25%, how low can LMN's price fall before you get a margin call? (Round your answer to 2 decimal places.)

c. How would your answer to (b) change if you had financed the initial purchase with only $19,750 of your own money? (Round your answer to 2 decimal places.)

d. What is the rate of return on your margined position (assuming again that you invest $30,000 of your own money) if LMN is selling after 1 year at: (i) $87.20; (ii) $79; (iii) $70.80? What is the relationship between your percentage return and the percentage change in the price of LMN? Assume that LMN pays no dividends. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

e. Continue to assume that a year has passed. How low can LMN's price fall before you get a margin call? (Round your answer to 2 decimal places.)

​Previously, 5​% of mothers smoked more than 21 cigarettes during their pregnancy. An obstetrician believes that the percentage of mothers who smoke 21 cigarettes or more is less than 5​% today. She randomly selects 130 pregnant mothers and finds that 5 of them smoked 21 or more cigarettes during pregnancy. Test the​ researcher's statement at the α=0.05 level of significance. Identify the correct null and alternative hypotheses.

H0​: p ()0.05

H1: p() 0.05

Use technology to find the​ P-value. P-value= ​(Round to three decimal places as​ needed.)

Is there sufficient evidence to support the​ obstetrician's statement? A.No​, because the​ P-value is greater than α there is not sufficient evidence to conclude that the percentage of mothers who smoke 21 or more cigarettes during pregnancy is less than 5​%, meaning we do not reject the null hypothesis. B.Yes​, because the​ P-value is greater than α there is sufficient evidence to conclude that the percentage of mothers who smoke 21 or more cigarettes during pregnancy is less than 5​%, meaning we do not reject the null hypothesis. C.No​, because the​ P-value is less than α there is not sufficient evidence to conclude that the percentage of mothers who smoke 21 or more cigarettes during pregnancy is less than 5​%, meaning we reject the null hypothesis. D. Yes​, because the​ P-value is less than α there is sufficient evidence to conclude that the percentage of mothers who smoke 21 or more cigarettes during pregnancy is less than 5​%, meaning we reject the null hypothesis.

​Previously, 5​% of mothers smoked more than 21 cigarettes during their pregnancy. An obstetrician believes that the percentage of mothers who smoke 21 cigarettes or more is less than 5​% today. She randomly selects 130 pregnant mothers and finds that 5 of them smoked 21 or more cigarettes during pregnancy. Test the​ researcher's statement at the α=0.05 level of significance. Identify the correct null and alternative hypotheses.

H0​: p()0.05

H1​: p()0.05

Use technology to find the​ P-value. P-value=() ​(Round to three decimal places as​ needed.)

Is there sufficient evidence to support the​ obstetrician's statement? A.No​, because the​ P-value is greater than α there is not sufficient evidence to conclude that the percentage of mothers who smoke 21 or more cigarettes during pregnancy is less than 5​%, meaning we do not reject the null hypothesis. B. Yes​, because the​ P-value is greater than α there is sufficient evidence to conclude that the percentage of mothers who smoke 21 or more cigarettes during pregnancy is less than 5​%, meaning we do not reject the null hypothesis. C. No​, because the​ P-value is less than α there is not sufficient evidence to conclude that the percentage of mothers who smoke 21 or more cigarettes during pregnancy is less than 5​%, meaning we reject the null hypothesis. D. Yes​, because the​ P-value is less than α there is sufficient evidence to conclude that the percentage of mothers who smoke 21 or more cigarettes during pregnancy is less than 5​%, meaning we reject the null hypothesis.

Suppose that LMN stock currently is selling at $78 per share. You buy 250 shares using $10,000 of your own money, borrowing the remainder of the purchase price from your broker. The rate on the margin loan is 5%.

a. What is the percentage increase in the net worth of your brokerage account if the price of LMN immediately changes to: (i) $84.24; (ii) $78; (iii) $71.76? What is the relationship between your percentage return and the percentage change in the price of LMN? (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

b. If the maintenance margin is 25%, how low can LMN's price fall before you get a margin call? (Round your answer to 2 decimal places.)

c. How would your answer to (b) change if you had financed the initial purchase with only $9,750 of your own money? (Round your answer to 2 decimal places.)

d. What is the rate of return on your margined position (assuming again that you invest $10,000 of your own money) if LMN is selling after 1 year at: (i) $84.24; (ii) $78; (iii) $71.76? What is the relationship between your percentage return and the percentage change in the price of LMN? Assume that LMN pays no dividends. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

e. Continue to assume that a year has passed. How low can LMN's price fall before you get a margin call? (Round your answer to 2 decimal places.)

Suppose that LMN stock currently is selling at $62 per share. You buy 300 shares using $12,000 of your own money, borrowing the remainder of the purchase price from your broker. The rate on the margin loan is 9%.

a. What is the percentage increase in the net worth of your brokerage account if the price of LMN immediately changes to: (i) $66.65; (ii) $62; (iii) $57.35? What is the relationship between your percentage return and the percentage change in the price of LMN? (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

b. If the maintenance margin is 25%, how low can LMN's price fall before you get a margin call? (Round your answer to 2 decimal places.)

c. How would your answer to (b) change if you had financed the initial purchase with only $9,300 of your own money? (Round your answer to 2 decimal places.)

d. What is the rate of return on your margined position (assuming again that you invest $12,000 of your own money) if LMN is selling after 1 year at: (i) $66.65; (ii) $62; (iii) $57.35? What is the relationship between your percentage return and the percentage change in the price of LMN? Assume that LMN pays no dividends. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

e. Continue to assume that a year has passed. How low can LMN's price fall before you get a margin call? (Round your answer to 2 decimal places.)

An organization monitors many aspects of elementary and secondary education nationwide. Their 2000 numbers are often used as a baseline to assess changes. In 2000 48 % of students had not been absent from school even once during the previous month. In the 2004 ​survey, responses from 6827 randomly selected students showed that this figure had slipped to 47 %. Officials would note any change in the rate of student attendance. Answer the questions below.

​(a) Write appropriate hypotheses.

Upper H 0 : The percentage of students in 2004 with perfect attendance the previous month ▼ is greater than 48%. is less than 48%. is different from 48%. is equal to 48%.

Upper H Subscript Upper A Baseline : The percentage of students in 2004 with perfect attendance the previous month ▼ is greater than 48%. is equal to 48%. is less than 48%. is different from 48%.

(b) Check the necessary assumptions.

The independence condition is ▼ satisfied. not satisfied. The randomization condition is ▼ not satisfied. satisfied. The​ 10% condition is ▼ satisfied. not satisfied. The​ success/failure condition is ▼ not satisfied. satisfied. ​

(c) Perform the test and find the​ P-value. ​P-value equals ________ ​(Round to three decimal places as​ needed.) ​

(d) State your conclusion. Assume a=0.05.

A. We fail to reject the null hypothesis. There is sufficient evidence to suggest that the percentage of students with perfect attendance in the previous month has changed.

B. We can reject the null hypothesis. There is sufficient evidence to suggest that the percentage of students with perfect attendance in the previous month has changed.

C. We fail to reject the null hypothesis. There is not sufficient evidence to suggest that the percentage of students with perfect attendance in the previous month has changed.

Q2. Proportions (percentages) in a Z Distribution

A large population of scores from a standardized test are normally distributed with a population mean (μ) of 50 and a standard deviation (σ) of 5. Because the scores are normally distributed, the whole population can be converted into a Z distribution. Because the Z distribution has symmetrical bell shape with known properties, it’s possible to mathematically figure out the percentage of scores within any specified area in the distribution. The Z table provides the percentages corresponding to any Z score.

a. John has a score of 55. What is John’s Z score?

b. What is the percentage of students that score lower than John?

c. Based on the Z table, if 1000 students take the test, how many of them would likely score above John’s score? (Round the answer to a whole number)

d. Tom has a score of 40. What is Tom’s Z score?

e. What is the percentage of students that score lower than Tom?

f. What is the percentage of students that score between John and Tom?

g. Based on the Z table, if 1000 students take the test, how many of them would likely score below Tom’s score?

h. Anna scores at the 99^th percentile on this exam, what is her Z score?

Hint: A score at 99^th percentile means 99% of the scores are below this score.

i. Based on the result of the previous question, what is Anna’s actual score on the exam?

j. What would be the median score on this exam?

Hint: Review the definition of “median” and then figure out the percentage of scores below (or above) this score.

Suppose that Xtel currently is selling at $44 per share. You buy 350 shares using $12,000 of your own money, borrowing the remainder of the purchase price from your broker. The rate on the margin loan is 9%

. a. What is the percentage increase in the net worth of your brokerage account if the price of Xtel immediately changes to: (i) $46.20; (ii) $44; (iii) $41.80? What is the relationship between your percentage return and the percentage change in the price of Xtel? (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) b. If the maintenance margin is 25%, how low can Xtel’s price fall before you get a margin call? (Round your answer to 2 decimal places.) c. How would your answer to (b) change if you had financed the initial purchase with only $7,700 of your own money? (Round your answer to 2 decimal places.) d. What is the rate of return on your margined position (assuming again that you invest $12,000 of your own money) if Xtel is selling after 1 year at: (i) $46.20; (ii) $44; (iii) $41.80? What is the relationship between your percentage return and the percentage change in the price of Xtel? Assume that Xtel pays no dividends. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) e. Continue to assume that a year has passed. How low can Xtel’s price fall before you get a margin call? (Round your answer to 2 decimal places.)