
Concept explainers
Uses
Hypothesis Testing with Two Samples Hypothesis testing enables you to determine whether differences in samples indicate actual differences in populations or are merely due to sampling error. For instance, a study conducted on about 1400 American children in a variety of settings compared the behavior of the children who attended day care with the behavior of those who stayed home. Aggressive behavior such as stealing toys, pushing other children, and starting fights was measured in both groups. The study showed that children who attended day care for more than 30 hours per week were about three times more likely to be aggressive than those who stayed home. Although the aggressive behavior observed in the study was well within the normal
Abuses
Confounding Variables The U.S. study found that the results were the same regardless of quality of the day care center and income of the family. However, the overall quality of care experienced by most of the children studied could be the problem—a survey of American day care centers that measured aspects such as number and expertise of caregivers found that only 10 percent of American day care centers provided high-quality care.
A similar study of preschoolers and aggressive behavior in Norway, where day care centers are subject to strict standards and the ratio of adult caregivers to children is high, found that the link between day care attendance and aggressive behavior was minimal. Another Norwegian study included an additional variable, differences between siblings, and found no relationship between day care attendance and behavior problems. These additional variables that are often out of the researcher’s control are known as confounding variables.
Study Funding A series of studies was conducted on various methods for reducing the number of cigarettes that smokers smoke. The study compared smokers who were simply told to smoke less and those who tried methods such as nicotine replacement therapy, electronic cigarettes, and using reduced tar, carbon, or nicotine cigarettes. Some methods were shown to be effective in reducing the number of cigarettes smoked.
Some of the studies were funded by the tobacco industry, which could profit from promoting strategies other than quitting as beneficial to smokers’ health. When dealing with statistics, it is always good to know who is paying for a study, and whether the researchers are unbiased.
1. Confounding Variables A pharmaceutical company has applied for approval to market a new arthritis medication. The research involved a test group that was given the medication and another test group that was given a placebo. Describe some possible confounding variables that could influence the results of the study.

To describe: The possible confounding variables that could influence the results of the study.
Answer to Problem 1UA
The possible confounding variables that could influence the results of the study are age and medical report.
Explanation of Solution
Given info:
The study based on the pharmaceutical company has applied for the approval to market a new arthritis medication.
Justification:
Confounding variable:
Confounding variable is a third variable that is associated with explanatory and response variables. In other words, confounding variable influences the response variable.
Here, the possible confounding variables that could influence the results of the study are age and medical report.
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Chapter 8 Solutions
Elementary Statistics: Picturing the World (7th Edition)
- a) Let X and Y be independent random variables both with the same mean µ=0. Define a new random variable W = aX +bY, where a and b are constants. (i) Obtain an expression for E(W).arrow_forwardThe table below shows the estimated effects for a logistic regression model with squamous cell esophageal cancer (Y = 1, yes; Y = 0, no) as the response. Smoking status (S) equals 1 for at least one pack per day and 0 otherwise, alcohol consumption (A) equals the average number of alcohoic drinks consumed per day, and race (R) equals 1 for blacks and 0 for whites. Variable Effect (β) P-value Intercept -7.00 <0.01 Alcohol use 0.10 0.03 Smoking 1.20 <0.01 Race 0.30 0.02 Race × smoking 0.20 0.04 Write-out the prediction equation (i.e., the logistic regression model) when R = 0 and again when R = 1. Find the fitted Y S conditional odds ratio in each case. Next, write-out the logistic regression model when S = 0 and again when S = 1. Find the fitted Y R conditional odds ratio in each case.arrow_forwardThe chi-squared goodness-of-fit test can be used to test if data comes from a specific continuous distribution by binning the data to make it categorical. Using the OpenIntro Statistics county_complete dataset, test the hypothesis that the persons_per_household 2019 values come from a normal distribution with mean and standard deviation equal to that variable's mean and standard deviation. Use signficance level a = 0.01. In your solution you should 1. Formulate the hypotheses 2. Fill in this table Range (-⁰⁰, 2.34] (2.34, 2.81] (2.81, 3.27] (3.27,00) Observed 802 Expected 854.2 The first row has been filled in. That should give you a hint for how to calculate the expected frequencies. Remember that the expected frequencies are calculated under the assumption that the null hypothesis is true. FYI, the bounderies for each range were obtained using JASP's drag-and-drop cut function with 8 levels. Then some of the groups were merged. 3. Check any conditions required by the chi-squared…arrow_forward
- Suppose that you want to estimate the mean monthly gross income of all households in your local community. You decide to estimate this population parameter by calling 150 randomly selected residents and asking each individual to report the household’s monthly income. Assume that you use the local phone directory as the frame in selecting the households to be included in your sample. What are some possible sources of error that might arise in your effort to estimate the population mean?arrow_forwardFor the distribution shown, match the letter to the measure of central tendency. A B C C Drag each of the letters into the appropriate measure of central tendency. Mean C Median A Mode Barrow_forwardA physician who has a group of 38 female patients aged 18 to 24 on a special diet wishes to estimate the effect of the diet on total serum cholesterol. For this group, their average serum cholesterol is 188.4 (measured in mg/100mL). Suppose that the total serum cholesterol measurements are normally distributed with standard deviation of 40.7. (a) Find a 95% confidence interval of the mean serum cholesterol of patients on the special diet.arrow_forward
- The accompanying data represent the weights (in grams) of a simple random sample of 10 M&M plain candies. Determine the shape of the distribution of weights of M&Ms by drawing a frequency histogram. Find the mean and median. Which measure of central tendency better describes the weight of a plain M&M? Click the icon to view the candy weight data. Draw a frequency histogram. Choose the correct graph below. ○ A. ○ C. Frequency Weight of Plain M and Ms 0.78 0.84 Frequency OONAG 0.78 B. 0.9 0.96 Weight (grams) Weight of Plain M and Ms 0.84 0.9 0.96 Weight (grams) ○ D. Candy Weights 0.85 0.79 0.85 0.89 0.94 0.86 0.91 0.86 0.87 0.87 - Frequency ☑ Frequency 67200 0.78 → Weight of Plain M and Ms 0.9 0.96 0.84 Weight (grams) Weight of Plain M and Ms 0.78 0.84 Weight (grams) 0.9 0.96 →arrow_forwardThe acidity or alkalinity of a solution is measured using pH. A pH less than 7 is acidic; a pH greater than 7 is alkaline. The accompanying data represent the pH in samples of bottled water and tap water. Complete parts (a) and (b). Click the icon to view the data table. (a) Determine the mean, median, and mode pH for each type of water. Comment on the differences between the two water types. Select the correct choice below and fill in any answer boxes in your choice. A. For tap water, the mean pH is (Round to three decimal places as needed.) B. The mean does not exist. Data table Тар 7.64 7.45 7.45 7.10 7.46 7.50 7.68 7.69 7.56 7.46 7.52 7.46 5.15 5.09 5.31 5.20 4.78 5.23 Bottled 5.52 5.31 5.13 5.31 5.21 5.24 - ☑arrow_forwardく Chapter 5-Section 1 Homework X MindTap - Cengage Learning x + C webassign.net/web/Student/Assignment-Responses/submit?pos=3&dep=36701632&tags=autosave #question3874894_3 M Gmail 品 YouTube Maps 5. [-/20 Points] DETAILS MY NOTES BBUNDERSTAT12 5.1.020. ☆ B Verify it's you Finish update: All Bookmarks PRACTICE ANOTHER A computer repair shop has two work centers. The first center examines the computer to see what is wrong, and the second center repairs the computer. Let x₁ and x2 be random variables representing the lengths of time in minutes to examine a computer (✗₁) and to repair a computer (x2). Assume x and x, are independent random variables. Long-term history has shown the following times. 01 Examine computer, x₁₁ = 29.6 minutes; σ₁ = 8.1 minutes Repair computer, X2: μ₂ = 92.5 minutes; σ2 = 14.5 minutes (a) Let W = x₁ + x2 be a random variable representing the total time to examine and repair the computer. Compute the mean, variance, and standard deviation of W. (Round your answers…arrow_forward
- The acidity or alkalinity of a solution is measured using pH. A pH less than 7 is acidic; a pH greater than 7 is alkaline. The accompanying data represent the pH in samples of bottled water and tap water. Complete parts (a) and (b). Click the icon to view the data table. (a) Determine the mean, median, and mode pH for each type of water. Comment on the differences between the two water types. Select the correct choice below and fill in any answer boxes in your choice. A. For tap water, the mean pH is (Round to three decimal places as needed.) B. The mean does not exist. Data table Тар Bottled 7.64 7.45 7.46 7.50 7.68 7.45 7.10 7.56 7.46 7.52 5.15 5.09 5.31 5.20 4.78 5.52 5.31 5.13 5.31 5.21 7.69 7.46 5.23 5.24 Print Done - ☑arrow_forwardThe median for the given set of six ordered data values is 29.5. 9 12 23 41 49 What is the missing value? The missing value is ☐.arrow_forwardFind the population mean or sample mean as indicated. Sample: 22, 18, 9, 6, 15 □ Select the correct choice below and fill in the answer box to complete your choice. O A. x= B. μεarrow_forward
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