Suppose 52% of the students in a university are baseball players. If a sample of

Question

Suppose 52% of the students in a university are baseball players. If a sample of 646 students is selected, what is the probability that the sample proportion of baseball players will be greater than 53%? 0.3055 0.3513 0.3332 0.6487 A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. He wants to construct the 90% confidence interval with a maximum error of 0.20 reproductions per hour. Assuming that the mean is 6.6 reproductions and the variance is known to be 4.46, what is the minimum sample size required for the estimate? 2974 329 274 302 NASA is conducting an experiment to find out the fraction of people who black out at G forces greater than 6. In an earlier study, the population proportion was estimated to be 0.36. How large a sample would be required in order to estimate the fraction of people who black out at 6 or more Gs at the 99% confidence level with an error of at most 0.02 3822 4041 3610 1648 What happens to the width of a confidence interval for a population mean if the level of confidence is increased without changing the sample size? Assume that the population standard deviation is unknown and the population distribution is approximately normal. Select your answer from the choices below. The margin of error will increase because the critical value will decrease. The increased margin of error will cause the confidence interval to be wider. The margin of error will decrease because the critical value will increase. The decreased margin of error will cause the confidence interval to be narrower.

Explanation / Answer

3) here std error=(p(!-p)/n)1/2 =0.0197

P(X>0.53) =1-P(X<(0.53-0.52)/0.0197) =1-P(Z<0.5087)=1-0.6945 =0.3055

option A is correct

4)for 90% CI, z=1.6449

hence sample size =(z*Std deviation/margin of error)2 =~302

5)here ro 99% CI, z=2.5758

hence sample size =p(1-p)(Z/margin of error )2=~3822

6)option B is OK

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