Assume that the college professor obtained a grant to study whether there was an improvement in the mathematics ability of freshmen. Using this grant money, he is able to obtain larger samples. The results are compiled in the following table. Last year This year Size of sample 125 100 Average score 562 568 Standard deviation 40 42 Can the professor reject the null hypothesis that the average scores improved? Use a 5 % level of significance.
2.1 Assume that the college professor obtained a grant to study whether there was an improvement in the mathematics ability of freshmen. Using this grant money, he is able to obtain larger samples. The results are compiled in the following table.
Last year
This year
Size of sample
125
100
Average score
562
568
Standard deviation
40
42
Can the professor reject the null hypothesis that the average scores improved? Use a 5 % level of significance.
2.2 In a recent poll, 800 voters were randomly sampled and asked whether they would approve of the building of an incinerator in the state. According to the poll, 450 voters approved and 350 voters disapproved. Is there enough evidence to argue that more than 50 % of the voters support the building of the incinerator?
Use a 5 % level of significance.
2.3 Suppose the Acme Drug Company develops a new drug, designed to prevent colds. The company states that the drug is equally effective for men and women. To test this claim, they choose a simple random sample of 100 women and 200 men from a population of 100,000 volunteers.
At the end of the study, 38% of the women caught a cold; and 51% of the men caught a cold. Based on these findings, can we reject the company's claim that the drug is equally effective for men and women? Use a 0.05 level of significance.
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