Show your work for each problem. Be sure to write confidence intervals appropria

Question

Show your work for each problem. Be sure to write confidence intervals appropriately; full calculator steps must be written with what you input in the calculator to earn credit. Null and Alternative hyptheses must be stated; ope of test - one tail left or right, or two tail; p-value or critical value and your decision made for #'s 3 and 4. I. A poll of 1235 US. drivers found 71% enjoyed driving their automobiles. Construct a 95 percent confidence interval for the proportion of all U.S. drivers who enjoy driving their cars. (25 points) 2. The body-mass index (BMI) of all American 20-something women is believed to follow a normal distribution with a standard deviation of 5.5. Find how many 20-something women should be randomly sampled if we want the mean BMI of such a sample to be within 1 BMI unit of the population mean with 95 percent confidence. 3. In tests of a computer component, it is found that the mean time between failures is 520 hours. A modification is made which is supposed to increase the time between failures. Tests on a random sample of 10 modified components resulted in the following times (in hours) between failures: 518 548 561 523 536 499 538 557 528 563 t the 0.05 significance level, test the claim that for the modified components, the mean time etween failures is greater than 520 hours. A supplier of 3.5" disks claims that no more than 1% of the disks are defective. In a random sample of 600 disks, it is found that 3% are defective, but the supplier claims that this is only a sample fluctuation. At the 0.01 level of significance, test the supplier's claim that no more than 1% are defective. 4,

Explanation / Answer

Solution:- given values  518,548,561,523,536,499,538,557,528,563

xbar = 537.1 s = 20.7013

hypothesises : H0: = 520 hrs.
H1: > 520 hrs.

  Test statistic: t = (537.1 - 520)/(20.7013/sqrt(10))

= 2.6122

  hence, computed z (2.6122) > critical z (1.645)

Reject Ho. There is sufficient evidence to support the claim that the mean is greater than 520 hours.

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