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Chapter 9: Q T9.5 (page 616)
A random sample of 100 likely voters in a small city produced 59 voters in favor of Candidate A. The observed value of the standardized test statistic for performing a test of
is which of the following?
a)
b)
c)
d)
e)
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How much juice? One company鈥檚 bottles of grapefruit juice are filled by a machine that is set to dispense an average of 180 milliliters (ml) of liquid. The company has been getting negative feedback from customers about underfilled bottles. To investigate, a quality-control inspector takes a random sample of 40 bottles and measures the volume of liquid in each bottle. The mean amount of liquid in the bottles is 179.6 ml and the standard deviation is 1.3 ml. Do these data provide convincing evidence at thesignificance level that the machine is underfilling the bottles?
The standardized test statistic for a test of versus isThis test is
a. not significant at either or
b. significant at but not at
c. significant atbut not at
d. significant at both and
e. inconclusive because we don鈥檛 know the value of
1 A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay for the upgrade. For the upgrade to be profitable, the company must sell it to more than of their customers. You contact a random sample of customers and find that would be willing to pay for the upgrade.
a. Do the sample data give convincing evidence that more than of the company鈥檚 customers are willing to purchase the upgrade? Carry out an appropriate test at the significance level.
b. Which would be a more serious mistake in this setting鈥攁 Type I error or a Type II error? Justify your answer.
c. Suppose that 30% of the company鈥檚 customers would be willing to pay for the upgrade. The power of the test to detect this fact is Interpret this value.
A milk processor monitors the number of bacteria per milliliter in raw milk received at the factory. A random sample of one-milliliter specimens of milk supplied by one producer gives the following data:
Construct and interpret a 90% confidence interval for the population mean 渭.
Two-sided test Suppose you want to perform a test of
versus at the significance level. A random sample
of size from the population of interest yields and
. Assume that the conditions for carrying out the test are met.
a. Explain why the sample result gives some evidence for the alternative hypothesis.
b. Calculate the standardized test statistic and P-value.
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