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Chapter 4: Problem 155

Print vs E-books Suppose you want to find out if reading speed is any different between a print book and an e-book. (a) Clearly describe how you might set up an experiment to test this. Give details. (b) Why is a hypothesis test valuable here? What additional information does a hypothesis test give us beyond the descriptive statistics we discussed in Chapter \(2 ?\) (c) Why is a confidence interval valuable here? What additional information does a confidence interval give us beyond the descriptive statistics of Chapter 2 and the results of a hypothesis test described in part (b)? (d) A similar study" has been conducted and reports that "the difference between Kindle and the book was significant at the \(p<.01\) level, and the difference between the iPad and the book was marginally significant at \(p=.06\)." The report also stated that "the iPad measured at \(6.2 \%\) slower reading speed than the printed book, whereas the Kindle measured at \(10.7 \%\) slower than print. However, the difference between the two devices [iPad and Kindle] was not statistically significant because of the data's fairly high variability." Can you tell from the first quotation which method of reading (print or e-book) was faster in the sample or do you need the second quotation for that? Explain the results in your own words.

Short Answer

Expert verified
An experiment can be setup with two groups reading the same content on print and e-books with time taken for reading being the primary measure. Hypothesis testing helps statistically confirm the observed difference. Confidence intervals provide a range estimate for the potential difference. The given study suggests that both e-reader and iPad users had slower reading speeds compared to print. The speed difference between the e-reader and iPad was not statistically significant.

Step by step solution

01

Experimental Setup

Define two groups of equal size with participants of diverse age and education background. Ensure that all participants are comfortable with using electronic reading devices. One group would read a specific content on a print book, the other on an e-book. Measure the time taken to read the content in both groups. Compare these timings to determine if there is a significant difference.
02

Importance of Hypothesis Test

A hypothesis test allows us to statistically compare the two groups' reading times. In this experiment, the null hypothesis might be that 'there is no difference between reading times for print and e-books'. If the p-value (probability of observing the data given the null hypothesis is true) is less than a pre-determined size (like 0.05), the null hypothesis is rejected.
03

Value of Confidence Interval

A confidence interval provides an estimated range of values which is likely to include an unknown population parameter. In this case, it gives a range of the difference between the average reading times of the print book group and the e-book group. The confidence interval provides additional context to the hypothesis test because it gives a plausible range of values for the difference, rather than just a yes/no answer.
04

Analyzing the Results

From the first quotation, we cannot definitively say which method of reading is faster, we only know there is a significant or marginally significant difference. From the second quotation, we learn that both the Kindle and the iPad were slower than the print book, with the iPad being slightly faster than the Kindle but not statistically significantly so.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Hypothesis Testing
Hypothesis testing is a crucial method in statistics used to determine if there is enough evidence in a sample of data to infer that a certain condition holds for the entire population. In the context of a reading speed experiment comparing print books and e-books, hypothesis testing can be incredibly revealing.

The process begins with formulating a null hypothesis ( H_0 ), which in this scenario could be "there is no difference in reading speed between print books and e-books." The alternative hypothesis ( H_a ) would suggest the contrary, that a significant difference does exist.

The primary goal is to test the validity of the null hypothesis by calculating the p-value, which reflects the probability of observing the results if the null hypothesis were true. If the p-value is below a predetermined threshold (commonly 0.05), we reject the null hypothesis, indicating a significant difference between the reading speeds of print and e-books.

Hence, hypothesis testing not only establishes statistical significance but also helps identify whether any observed differences in reading times are due to chance or are statistically noteworthy. This adds depth to the descriptive statistics, which merely summarize the data without drawing any inferences about populations.
Confidence Interval
A confidence interval is a range of values that is used to estimate a population parameter. It is an essential tool in statistics that provides more insight than simply stating a result in terms of hypothesis testing.

For a reading speed experiment, once a significant difference is identified between print books and e-books, a confidence interval can give us a range within which the true difference in reading speeds is likely to fall. For example, if you find the average reading speed for print books is X and for e-books is Y, a confidence interval might suggest that the true difference in reading speeds is between some values.

This interval, usually expressed with a certain confidence level (like 95%), allows researchers to understand the precision and reliability of their estimate. While hypothesis testing tells us if a difference exists, the confidence interval quantifies the size of this difference, providing a clearer picture of the magnitude and importance of the findings.
  • It adds context to hypothesis testing results.
  • It indicates the variability of the data.
  • It defines the range of plausible values.
Descriptive Statistics
Descriptive statistics serve as the foundation of any statistical analysis, providing simple summaries about the sample and measures. In a reading speed experiment, descriptive statistics would include average reading speeds, standard deviation, minimum and maximum values, and other central tendency measures, for both print and e-books.

These statistics offer a quick way to understand the data at a surface level by using numerical summaries and visualizations. By capturing the mean reading speed for each group and their variability, it becomes easier to describe the basic features of the dataset before moving on to more complex analyses.

Descriptive statistics lay the groundwork for further procedures like hypothesis testing and confidence intervals. Although they do not allow for any definite conclusions about the population, they provide the necessary insights to formulate hypotheses and set up experiments. They allow us to capture trends and patterns within the dataset, which are crucial for making informed judgments about data.

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Most popular questions from this chapter

Two p-values are given. Which one provides the strongest evidence against \(\mathrm{H}_{0} ?\) p-value \(=0.007 \quad\) or \(\quad\) p-value \(=0.13\)

Price and Marketing How influenced are consumers by price and marketing? If something costs more, do our expectations lead us to believe it is better? Because expectations play such a large role in reality, can a product that costs more (but is in reality identical) actually be more effective? Baba Shiv, a neuroeconomist at Stanford, conducted a study \(^{21}\) involving 204 undergraduates. In the study, all students consumed a popular energy drink which claims on its packaging to increase mental acuity. The students were then asked to solve a series of puzzles. The students were charged either regular price \((\$ 1.89)\) for the drink or a discount price \((\$ 0.89)\). The students receiving the discount price were told that they were able to buy the drink at a discount since the drinks had been purchased in bulk. The authors of the study describe the results: "the number of puzzles solved was lower in the reduced-price condition \((M=4.2)\) than in the regular-price condition \((M=5.8) \ldots p<0.0001 . "\) (a) What can you conclude from the study? How strong is the evidence for the conclusion? (b) These results have been replicated in many similar studies. As Jonah Lehrer tells us: "According to Shiv, a kind of placebo effect is at work. Since we expect cheaper goods to be less effective, they generally are less effective, even if they are identical to more expensive products. This is why brand-name aspirin works better than generic aspirin and why Coke tastes better than cheaper colas, even if most consumers can't tell the difference in blind taste tests." 22 Discuss the implications of this research in marketing and pricing.

Clicker Questions A statistics instructor would like to ask "clicker" questions that about \(80 \%\) of her students in a large lecture class will get correct. A higher proportion would be too easy and a lower proportion might discourage students. Suppose that she tries a sample of questions and receives 76 correct answers and 24 incorrect answers among 100 responses. The hypotheses of interest are \(H_{0}: p=0.80\) vs \(H_{a}: p \neq 0.80 .\) Discuss whether or not the methods described below would be appropriate ways to generate randomization samples in this setting. Explain your reasoning in each case. (a) Sample 100 answers (with replacement) from the original student responses. Count the number of correct responses. (b) Sample 100 answers (with replacement) from a set consisting of 8 correct responses and 2 incorrect responses. Count the number of correct responses.

Exercise and the Brain It is well established that exercise is beneficial for our bodies. Recent studies appear to indicate that exercise can also do wonders for our brains, or, at least, the brains of mice. In a randomized experiment, one group of mice was given access to a running wheel while a second group of mice was kept sedentary. According to an article describing the study, "The brains of mice and rats that were allowed to run on wheels pulsed with vigorous, newly born neurons, and those animals then breezed through mazes and other tests of rodent IQ"10 compared to the sedentary mice. Studies are examining the reasons for these beneficial effects of exercise on rodent (and perhaps human) intelligence. High levels of BMP (bone- morphogenetic protein) in the brain seem to make stem cells less active, which makes the brain slower and less nimble. Exercise seems to reduce the level of BMP in the brain. Additionally, exercise increases a brain protein called noggin, which improves the brain's ability. Indeed, large doses of noggin turned mice into "little mouse geniuses," according to Dr. Kessler, one of the lead authors of the study. While research is ongoing in determining which effects are significant, all evidence points to the fact that exercise is good for the brain. Several tests involving these studies are described. In each case, define the relevant parameters and state the null and alternative hypotheses. (a) Testing to see if there is evidence that mice allowed to exercise have lower levels of BMP in the brain on average than sedentary mice (b) Testing to see if there is evidence that mice allowed to exercise have higher levels of noggin in the brain on average than sedentary mice (c) Testing to see if there is evidence of a negative correlation between the level of BMP and the level of noggin in the brains of mice

In Exercises 4.14 and \(4.15,\) determine whether the sets of hypotheses given are valid hypotheses. State whether each set of hypotheses is valid for a statistical test. If not valid, explain why not. (a) \(H_{0}: \mu=15 \quad\) vs \(\quad H_{a}: \mu \neq 15\) (b) \(H_{0}: p \neq 0.5 \quad\) vs \(\quad H_{a}: p=0.5\) (c) \(H_{0}: p_{1}p_{2}\) (d) \(H_{0}: \bar{x}_{1}=\bar{x}_{2} \quad\) vs \(\quad H_{a}: \bar{x}_{1} \neq \bar{x}_{2}\)
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