Q1. An independent consumer group published its finding that the lifetimes of electric bulbs manufactured by BIG
Question:
Q1.
An independent consumer group published its finding that the lifetimes of electric bulbs manufactured by BIG Corporation are approximately normally distributed with a mean of 610 days and a variance of 14,520.25. BIG Corporation claims that the variance of its electric bulbs is less than 14,520.25. Suppose that we want to carry out a hypothesis test to see if BIG Corporation's claim is correct. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test.
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Q2.
The mean SAT score in mathematics is 509. The standard deviation of these scores is 36. A special preparation course claims that the mean SAT score, ,of its graduates is greater than 509. An independent researcher tests this by taking a random sample of 90 students who completed the course; the mean SAT score in mathematics for the sample was 518. At the 0.05 level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than 509? Assume that the population standard deviation of the scores of course graduates is also 36.
Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places, and round your responses as specified below.
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Q3.
An old medical textbook states that the mean sodium level for healthy adults is 138 mEq per liter of blood. A medical researcher believes that, because of modern dietary habits, the mean sodium level for healthy adults, , now differs from that given in the textbook. A random sample of 35 healthy adults is evaluated. The mean sodium level for the sample is 137 mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is 11 mEq. Assume that the population is normally distributed. Can we conclude, at the
0.01 level of significance, that the population mean adult sodium level differs from that given in the textbook?
Perform a two-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places, and round your responses as specified below.
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Q4.
An electronics manufacturing process has historically had a mean completion time of 70 minutes. It is claimed that, due to improvements in the process, the mean completion time, , is now less than 70 minutes. A random sample of 15 completion times using the new process is taken. The sample has a mean completion time of 65
minutes, with a standard deviation of 8 minutes.
Assume that completion times using the new process are approximately normally distributed. At the 0.05
level of significance, can it be concluded that the population mean completion time using the new process is less than 70 minutes?
Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)
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Q5.
Thanks to an initiative to recruit top students, an administrator at a college claims that this year's entering class must have a greater mean IQ score than that of entering classes from previous years. The administrator tests a random sample of 15 of this year's entering students and finds that their mean IQ score is
118, with a standard deviation of 14. The college records indicate that the mean IQ score for entering students from previous years is 111.
Is there enough evidence to conclude, at the 0.10 level of significance, that the population mean IQ score, , of this year's class is greater than that of previous years? To answer, assume that the IQ scores of this year's entering class are approximately normally distributed.
Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places.
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Expert Answer:
