# Hypothesis: difference between proportions, Chi square test

1 ) The college newspaper of a large midwestern university periodically conducts a survey of students on campus to determine the attitude on campus concerning issues of interest. Pictures of the studens interviewed by a reporter roaming the campus who selects students to interview haphazardly. On a particular day the reporter interviews eight students and askd them if they feel there is adequate student parking on campus. Five of the students say no.

The sample proportion p^ who respond no is

A) .375

B) .625

C).667

D) .700

2) Wich of the following assumptions for inference about a proportion using a confidence interval are violated in this example?

A) The data are an SRS from the population of interest.

B) The population is at least 10 times as large as the sample.

C) We are interested in inference about a proportion.

D) There appear to be no violations

A recent book noted that only 20% of investment managers out perfrom the standard indexes, such as Dow Jones Industrial Average onr the NASDAQ, overa a five year period. A sample of 200 investment managers that had graduated from one of the top 10 Business programs in the country were followed over a 5 year period. 50 of the outperformed the Dow Jones. Let p represent the probability that a random investment manager who graduated from one of the top 10 Business programs will out perform the Dow Jones over a 5 year period. Suppose you withed to see if there is evidence that graduates of one of the top business programs perform better thatn other investment managers. To do this, you test the hypothesis: Ho:p=0.20 vs. Ha:p>.20. The P-value of your test is

A) between .10 and .05

B) between .05 and .01

C) between .01 and .001

D) below .001

3) In alarge midwestern university ( the class of entering freshmen being on the order of 6000 or more student), an SRS of 100 entering freshmen in 1993 found that 20 finished in the bottom third of their high school class. Andmissions standards at the university were tightened in 1995. In 1997 an SRS of 100 entering freshmen found that 10 finsihed in the bottom 1/3 of thier high schoool class.Letting p1 and p2 be the proportion of all entering freshmen in 1993 and 1997, respectivley who graduated in the bottom third of their high school class. Is there evidence that the proportion of freshmen who graudated in the bottom third of their high school class in 1997 has been reduced, as a result of the tougher admission standards adopted in 1995. compared to the proportion in 1993? To determine this , you test the hypothesis: Ho:p1 = p2 vs. Ha:p1>p2. The P-value of your test is

A) beween.10 and .05

B) between .05 and .01

C) between .01 and .001

D) below .001

4) Are avid readers morelikely to wear glasses than those who read less frequently? 300 men in the Korean army were slected at random and characterized as to whether they wore glasses and whether the amount of reading they did was above, average or belwo averae. The reuslts are presented inthe following table.

Wear Glasses

Amount of Reading Yes No

Above Average 47 26

Average 48 78

Below Average 31 70

The numerical value of the chi-square statistic for testing independence of whether yuo wear glasses of the amount of reading you do is

A) 2

B) 8.65

C) 21

D) 30.7

5) Recent revenue shortfalls in a midwestern state led to a reduction inthe state budget for higher edcuation. To offset the reduction, the largest state university proposed a 25% tuition increase. It was determined that such and increase was needed to simply compensate for the lost support fromthe state. Random samples of 50 freshmen, 50 sophmores, 50 juniors, and 50 seniros from the university were asked whether or not they wre strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget as current levels. The results are given in the following talbe.

Year

Stronly Opposed Fresh Soph Jun Sen

Yes 39 36 29 18

No 11 14 21 32

What hypothesis are being tested by the chi-square test?

A) The null hypothesis is that year in school and whether or not you are stonly opposed are independent, and the alternative is that they are dependent.

B) The null hypothesis is that the mean number of who are stonly opposed is the same for each of the 4 yars, and the alternative is that these means are different.

C) The null hypothesis is that the distribution of the number who are stonly opposed versus not stronly opposed are the same for the 4 years.. The alternative says that these distribution are different.

D) The null hypothesis is that the distribution of the total number of students sampled in each of the 4 years are the same. The alternative is that these distributions are different.

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#### Solution Summary

Tests hypothesis for difference between proportions, performs a Chi square test.

Statistics: Difference in proportion of viewers watching three TV channels

In Los Angeles there are three network television stations, each with it own evening news program from 6:00 to 6:30 PM. According to a report in this morning's local newspaper, a random sample of 150 viewers last night revealed 53 watched the news on KNBC (channel 2), 64 watched KABC (channel 7), and 33 viewed KCBS (channel 2). At the 0.05 significance level, is there a difference in the proportion of viewers watching the three channels?

1. State the null and alternative hypothesis.

2. Identify the level of significance: Given at 0.05

3. Calculate the test statistic

4. Formulate the decision rule.

5. Make a decision.

See attached file.

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