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Exam 12: Asking and Answering Questions About a Population Mean

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Question 21

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Question 22

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At the Billy Goat Gruff Inn, machines are set to dispense 600 ml of soda into everycustomer's glass. Over time, however, the machine can get "out of control" and dispense toomuch soda or too little. The machine needs adjustment if the mean amount dispensed isdifferent than 600 ml. At a randomly selected time each clock hour, the owner dispenses andchecks a glass of soda and determines the actual volume of soda dispensed. One day thevolumes (in ml) of the dispensed soda were: Is there sufficient evidence to conclude that the dispensing machine needs adjustment?

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The level of significance of a test is the probability of making a type Ierror.

Describe in a few sentences how each of the following affects the power of a test: a) The size of the difference between the actual value and the hypothesized value ofthe population mean. b) The significance level, ? c) The sample size

In a few sentences, describe the difference between statistical and practicalsignificance.

A random sample of size n = 36 is selected from a population with mean µ= 50 andstandard deviation ? =12 . Determine the mean and standard deviation of thesampling distribution of $\bar{x}$ .

Many national parks, wildlife refuges, and wilderness areas lie directly below designatedmilitary air space. This raises issues of whether wildlife and loud jet noises are compatible.In an effort to evaluate the effects of low-altitude jet-noise, researchers simulated thesenoises for a representative sample of captive desert mule deer. Three minutes after the loudnoises were played, the heart rates (beats per minute) of these animals was measured, withthe following results: a) Calculate and interpret a 95% confidence interval for the mean heart rate 3 minutes afterloud jet noises. b) The usual mean heart rate for desert mule deer is about 51.2 beats per minute. Does theconfidence interval in part (a) support the view that the loud jet noise has some lingeringeffect on the heart rate of desert mule deer? Explain, using appropriate statisticallanguage.

One indicator of the health of field mice is the length of their tails. The followingdata on tail length (in mm) were gathered from a representative sample of field micenear Fairfield, Iowa. A biologist would like to construct a 95% confidence intervalfor the population mean tail length of the field mice near Fairfield. a) Using a graphical display of your choice, display the data in a way that will allowyou to determine whether it would be appropriate to use a t confidence interval toestimate the population mean. b) Using the graphical display from part (a), would you advise that constructing a tconfidence interval is appropriate? Explain the basis of your recommendation.

Describe in a few sentences how each of the following affects the power of a test: a) The size of the difference between the actual value and the hypothesized value ofthe population mean. b) The significance level, ? c) The sample size

A company provides portable walkie-talkies to construction crews. Their batteries last, onaverage, 55 hours of continuous use. The purchasing manager receives a brochureadvertising a new brand of batteries with a lower price, but suspects that the lifetime of thebatteries may be shorter than the brand currently in use. To test this, 8 randomly selectednew brand batteries are installed in the same model radio. Here are the results for thelifetime of the batteries (in hours): Is there sufficient evidence to conclude that the purchasing manager is correct in hisconjecture that the new brand has a shorter average lifetime?

When performing hypothesis tests, there are assumptions that must be met in order for the testto be appropriate. Describe the assumptions associated with a hypothesis test about apopulation mean when the sample size is small. For any assumptions that can be checkedusing sample data, describe how the check would be performed.