Suppose that in a class, there are n many boys and n many girls. Among these 2n many people, we will choose n many people. Counting in two different ways, show that Σ()=(*)
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- A pharmaceutical company has developed a new drug to help relieve acid reflux. However, as with all new drugs, there are concerns about adverse side effects. To check this, the company administers the drug to n randomly chosen people with acid reflux, and it finds that k of them experience adverse side effects. The company hopes to reject the null hypothesis that the proportion of drug-takers who experience adverse side effects is at least 0.5%. Which of the following is true? a. If n=1,250 and k=1, this is enough evidence to reject the null at the 1% level. b. If n=1,000 and k=3, this is enough evidence to reject the null at the 10% level. c. If n=4,000 and k=9, this is enough evidence to reject the null at the 1% level. d. If n=1,600 and k=4, this is enough evidence to reject the null at the 5% level.A producer of pocket calculators purchases the main processor chips in lots of1,000. The producer would like to have a 1 percent rate of defectives but willnormally not refuse a lot unless it has 4 percent or more defectives. Samples of50 are drawn from each lot, and the lot is rejected if more than two defectives arefound.a. What are p0, p1, n, and c for this problem?Suppose in a Country Waffleland, there are two socio-economic classes. The workingclass accounts for 90% of the population. Each person in the working class has awealth of w, where w > 0. The rest of the society consists of people with inheritedwealth. Each person in this class has a wealth of 9w. What is the Gini coefficientof the wealth distribution in this country?
- A city official claims that the proportion of all commuters who are in favor of an expanded public transportation system is 50%. A newspaper conducts a survey to determine whether this proportion is different from 50%. Out of 225 randomly chosen commuters, the survey finds that 99 of them reply yes when asked if they support an expanded public transportation system. Test the official’s claim at α= 0.05.Marine biologists have noticed that the color of the outermost growth band on a clam tends to be related to the time of year in which the clam dies. A biologist conducted a small investigation of whether this is true for the species Protothaca staminea. She collected a sample of 55 clam shells in February and 55 clam shells in March. 14 of the shells from February had a dark color on the outermost growth band, whereas 8 of the shells from March had a dark color on the outermost growth band. Carry out a hypothesis test to see if there is a difference in the proportion of shells with a dark outermost growth band between the two months; specifically, if the population proportion in February is higher than March. Let ? = 0.1.Note: Do all calculations as February - MarchA) The point estimate for the true difference in proportion of dark growth bands between February and March is: Note: answer using 4 decimal precisionB) The test statistic, ztest, is: Note: answer using 2 decimal…Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 150 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. a) State the appropriate null and alternate hypotheses. b) Find the P-value. c) Should a change be made?
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