Sampling shoppers A marketing consultant observes consecutive shoppers at a supermarket, recording how much each shopper spends in the store. Explain why it would not be wise to use these data to carry out a significance test about the mean amount spent by all shoppers at this supermarket.
Given in the question that, A marketing consultant observes consecutive shoppers at a supermarket, we have to Explain why it would not be wise to use these data to carry out a significance test about the mean amount spent by all shoppers at this supermarket.
A convenient sample is a non-probability sampling method in which the sample is taken from a group of people who are easy to touch or encounter. A convenience survey, for example, would entail standing outside a mall or a grocery store and asking customers to complete questionnaires. This kind of sampling is also known as grab sampling or availability sampling. The poll is a choice study, as the shoppers were chosen because they were "conveniently" consecutive.
There would also be shoppers who went shopping on the same day of the week and at the same time, implying that a segment of the population was left out.
Haemoglobin is a protein in red blood cells that carries oxygen from the lungs to body tissues. People with less than 12 grams of haemoglobin per deciliter of blood (g/dl) are anaemic. A public health official in Jordan suspects that Jordanian children are at risk of anaemia. He measures a random sample of 50 children.
“I can’t get through my day without coffee” is a common statement from many students. Assumed benefits include keeping students awake during lectures and making them more alert for exams and tests. Students in a statistics class designed an experiment to measure memory retention with and without drinking a cup of coffee one hour before a test. This experiment took place on two different days in the same week (Monday and Wednesday). Ten students were used. Each student received no coffee or one cup of coffee, one hour before the test on a particular day. The test consisted of a series of words flashed on a screen, after which the student had to write down as many of the words as possible. On the other day, each student received a different amount of coffee (none or one cup). (a) One of the researchers suggested that all the subjects in the experiment drink no coffee before Monday’s test and one cup of coffee before Wednesday’s test. Explain to the researcher why this is a bad idea and suggest a better method of deciding when each subject receives the two treatments.
(b) The data from the experiment are provided in the table below. Set up and carry out an appropriate test to determine whether there is convincing evidence that drinking coffee improves memory.
A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of one inch could be increased by
(a) using only volunteers from the basketball team in the experiment.
(b) using instead of .
(c) using instead of .
(d) giving the drug to randomly selected students instead of .
(e) using a two-sided test instead of a one-sided test.
Spinning for apples (6,3 or 7.3) In the "Ask Marilyn" column of Parade magzine, a reader posed this question: "Say that a slot machine has five wheels, and each wheel has five symbols: an apple, a grape, a peach, a pear, and a plum. I pull the lever five times. What are the chances that I'll get at least one apple?" Suppose that the wheels spin independently and that the fre symbols are equally likely to appear on each wheel in a given spin.
(a) Find the probability that the slot player gets at least one apple in one pull of the lever. Show your method clearly.
(b) Now answer the reader's question. Show your method clearly.
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 needs to sell it to more than of their customers. You contact a random sample of customers and find that 16 would be willing to pay for the upgrade.
(a) Do the sample data give good evidence that more than of the company’s 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—a Type I error or a Type II error? Justify your answer.
(c) Other than increasing the sample size, describe one way to increase the power of the test in (a).
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