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Chapter 12: Q. 14 (page 801)

Do hummingbirds prefer store-bought food made from concentrate or a simple mixture of sugar and water? To find out, a researcher obtains 10identical hummingbird feeders and fills 5, chosen at random, with store-bought food from concentrate and the other 5with a mixture of sugar and water. The feeders are then randomly assigned to10possible hanging locations in the researcher鈥檚 yard. Which inference procedure should you use to test whether hummingbirds show a preference for store-bought food based on amount consumed?

(a) A one-sample z test for a proportion .

(b) A two-sample z test for a proportion .

(c) A chi-square test for association/independence .

(d) A two-sample t test .

(e) A paired t test .

Short Answer

Expert verified

(d) A two-sample t test .

Step by step solution

01

Given information.

We have been given that,

Number of identical hummingbirds feeders = 10

Number of feeders filled with store bought food = 5

Number of feeders filled with sugar mixture = 5

We need find the procedure for store bought food based on amount consumed.

02

Simplify.

Feeder 1: Sugar/Water, for consumed amount.

Feeder 2: Store bought , for consumed amount.

There are definitely two populations. You will not use the Z test for proportion as that assumes a large sample size of which 10feeders are not.

The chi square test for independence would not be useful because we only have 1factor ( sugar water or store bought).

A paired T test is not useful since the observations are not paired in any way.

Therefore, the best answer is (d) a two - sample t test, but because this is a small sample ,it is vitally important the population is normally distributed which may or may not be the case.

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Most popular questions from this chapter

An old saying in golf is 鈥淵ou drive for show and you putt for dough.鈥� The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69of the nearly 1000players on the PGA Tour鈥檚 world money list are examined. The average number of putts per hole and the player鈥檚 total winnings for the previous season is recorded. A least-squares regression line was fitted to the data. The following results were obtained from statistical software.

Suppose that the researchers test the hypotheses H0:尾=0: Ha:尾<0. The value of the t statistic for this test is

(a)2.61

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A major agricultural company is testing a newvariety of wheat to determine whether it is more resistant tocertain insects than is the current wheat variety. The pro-portion of a current wheat crop lost to insects is 4%. Thus,the company wishes to test the following hypotheses:

H0:p=0.04

H0:p<0.04

Which of the following significance levels and sample sizes

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(b)n=400and伪=0.05

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Some college students collected data on the intensity of light at various depths in a lake. Here are their data:

Depth (meters)Light intensity (lumens)5168.006120.42786.31861.87944.341031.781122.78

(a) Make a reasonably accurate scatterplot of the data by hand, using depth as the explanatory variable. Describe what you see.

(b) A scatterplot of the natural logarithm of light intensity versus depth is shown below. Based on this graph, explain why it would be reasonable to use an exponential model to describe the relationship between light intensity and depth.

Minitab output from a linear regression analysis on the transformed data is shown below

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(c) Give the equation of the least-squares regression line. Be sure to define any variables you use.

(d) Use your model to predict the light intensity at a depth of 12 meters. The actual light intensity reading at that depth was 16.2 lumens. Does this surprise you? Explain

The swinging pendulum Refer to Exercise 33. Here is Minitab output from separate regression analyses of the two sets of transformed pendulum data:

Do each of the following for both transformations.

(a) Give the equation of the least-squares regression line. Define any variables you use.

(b) Use the model from part (a) to predict the period of a pendulum with length of 80 centimeters. Show your work.

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A residual plot from the least-squares regression is shown below. Which of the following statements is supported by the graph

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(d) For two players, the regression line under predicts their total winnings by more than\)800,000.

(e) The residual plot reveals a strong positive correlation between average putts per round and prediction errors from the least-squares line for these players.
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