### Critical Values of the Pearson Correlation Coefficient rThis table presents the critical values of the Pearson Correlation Coefficient \( r \) for significance levels \(\alpha = 0.05\) and \(\alpha = 0.01\). These critical values are used in hypothesis testing to determine if there is a statistically significant linear relationship between two variables.**Columns Explanation:**- **n**: Sample size- **α = 0.05**: Critical value of \( r \) for a significance level of 0.05- **α = 0.01**: Critical value of \( r \) for a significance level of 0.01**How to Use this Table:**To test the null hypothesis \( H_0: ρ = 0 \) against the alternative hypothesis \( H_1: ρ ≠ 0 \):1. Calculate the Pearson correlation coefficient \( r \) from your sample data.2. Select the appropriate critical value from the table based on your sample size \( n \) and desired significance level (\(\alpha = 0.05\) or \(\alpha = 0.01\)).3. Reject the null hypothesis \( H_0 \) if the absolute value of \( r \) is greater than the critical value in the table.**Table of Critical Values:**| n | α = 0.05 | α = 0.01 ||-----|----------|----------|| 4 | 0.950 | 0.990 || 5 | 0.878 | 0.959 || 6 | 0.811 | 0.917 || 7 | 0.754 | 0.875 || 8 | 0.707 | 0.834 || 9 | 0.666 | 0.798 || 10 | 0.632 | 0.765 || 11 | 0.602 | 0.735 || 12 | 0.576 | 0.708 || 13 | 0.553 | 0.684 || 14 | 0.532 | 0.661 || 15 | ### Linear Regression and Predictive Analysis Based on IQ Scores#### Scenario:Suppose IQ scores were obtained for 20 randomly selected sets of couples. The 20 pairs of measurements yield the following statistics:- The average IQ score (\(\bar{x}\)) of the wives: 99.05- The average IQ score (\(\bar{y}\)) of the husbands: 100.15- Pearson correlation coefficient (\(r\)): 0.837- P-value: 0.000- Regression line equation: \(\hat{y} = 19.19 + 0.82x\), where \(x\) represents the IQ score of the wife.#### Task:Find the best predicted value of \(\hat{y}\) given that the wife has an IQ of 108. Use a significance level of 0.05.Click the icon to view the critical values of the Pearson correlation coefficient \( r \).Input the best predicted value of \(\hat{y}\) below:(Please round to two decimal places as needed.)\[ \hat{y} = \: \_\_\_\_\_ \]#### Solution Steps:1. **Substitute the wife's IQ score in the regression equation**: Given the regression equation \(\hat{y} = 19.19 + 0.82x\), and the wife's IQ score \(x = 108\). 2. **Calculate the predicted value**: \[ \hat{y} = 19.19 + 0.82 \times 108 \] 3. **Solve the equation to find \(\hat{y}\)**: \[ \hat{y} = 19.19 + 88.56 = 107.75 \]4. **Write the final predicted value**: The best predicted value of \(\hat{y}\) is **107.75**.This concludes the analysis of the predicted IQ score for the husband based on the given wife's IQ score using the linear regression model.

The question is about regression Given : No. of sets of couples ( n ) = 20 x¯ = 99.05 y¯ = 100.15 r…

Answered: Suppose IQ scores were obtained for 20…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose IQ scores were obtained for 20 randomly selected sets of couples. The 20 pairs of measurements yield x = 98.91, y = 99, r= 0.937, P-value = 0.000, and y = 5.67 + 0.94x, where x represents the IQ score of the wife. Find the best predicted value of y given that the wife has an IQ of 95? Use a significance level of 0.05. Click the icon to view the critical values of the Pearson correlation coefficient r. The best predicted value of y is (Round to two decimal places as needed.)
The mean GPA for a 127 residents of the local apartment complex is 1.6. What is the best point estimate for the mean GPA for all the residents of the local apartment complex?
The IQ scores for a random sample of subjects with medium lead levels in their blood and another random sample of subjects with high lead levels in their blood are given below. Use a 0.05 significance level to test the claim that subjects with medium lead levels have full IQ scores with a higher median that the median full IQ score for subjects with high lead levels. Does lead level appear to affect full IQ scores? Click the icon to view the data table. First define the null and alternative hypotheses. Ho: H₁: Data Table Let the medium lead level be sample 1. Medium Lead High Lead Level Level 66 98 64 87 63 HR22CTCTETUE 2 13 100 83 84 84 70 73 70 78 91 61 72 88 73 76 63 66 61 64 61 66 92 76 107 66 X
The accompanying table gives amounts of arsenic in samples of brown rice from three different states. The amounts are in micrograms of arsenic and all samples have the same serving size. The data are from the Food and Drug Administration. Use a 0.05 significance level to test the claim that the three samples are from populations with the same mean. Do the amounts of arsenic appear to be different in the different states? Given that the amounts of arsenic in the samples from Texas have the highest mean, can we conclude that brown rice from Texas poses the greatest health problem? Click the icon to view the data. Arsenic Amounts Arkansas California Texas Determine the test statistic. 4.81 4.91 5.02 5.44 5.44 5.42 5.63 5.61 5.63 5.86 5.96 6.06 1.45 3.66 4.04 4.49 4.93 5.08 5.29 5.43 5.42 5.46 5.58 5.55 5.57 5.78 6.64 6.93 6.89 6.85 7.09 7.30 7.49 7.55 7.71 7.72 The test statistic is (Round to two decimal places as needed.) Print Done
Suppose IQ scores were obtained for 20 randomly selected sets of couples. The 20 pairs of measurements yield x = 98.46, y = 99.4, r=0.883, P-value = 0.000, and y=-14.65 +1.16x, where x represents the IQ score of the wife. Find the best predicted value of y given that the wife has an IQ of 101? Use a significance level of 0.05. Click the icon to view the critical values of the Pearson correlation coefficient r. The best predicted value of y is (Round to two decimal places as needed.)
Only letters C and D
The indicated IQ score, x, is
The accompanying table gives amounts of arsenic in samples of brown rice from three different states. The amounts are in micrograms of arsenic and all samples have the same serving size. The data are from the Food and Drug Administration. Use a 0.05 significance level to test the claim that the three samples are from populations with the same mean. Do the amounts of arsenic appear to be different in the different states? Given that the amounts of arsenic in the samples from Texas have the highest mean, can we conclude that brown rice from Texas poses the greatest health problem? Click the icon to view the data. What are the hypotheses for this test? O A. Ho: At least one of the means is different from the others H₁ H₁ H₂ H3 OB. Ho: H₁ H₂=H3 H₁: At least one of the means is different from the others OC. Ho: H₁ H₂=H3 H₁: H₁ H₂ #H3 O D. Ho: M₁ #₂ #H3 H₁: H₁ H₂=H3 Determine the test statistic. The test statistic is (Round to two decimal places as needed.) Determine the P-value. The P-value…
The accompanying data set includes volumes (ounces) of a sample of cans of regular Coke. The summary statistics are n = 36, x = 12.199 oz, s = 0.100 oz. Assume that a simple random sample has been selected. Use a 0.01 significance level to test the claim that cans of Coke have a mean volume of 12.00 ounces. Does it appear that consumers are being cheated? Click the icon to view the data set of regular Coke can volumes. Identify the null and alternative hypotheses. Ho: H₁: (Type integers or decimals. Do not round.) Identify the test statistic. (Round to two decimal places as needed.) Identify the P-value. (Round to three decimal places as needed.) State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Decide whether it appears that consumers are being cheated. the null hypothesis. There because consumers are getting sufficient evidence at the 0.01 significance level to 12.00 ounces. the claim that cans of Coke have a mean…
A doctor wanted to determine whether there is a relation between a male’s age and his HDL (so-called good cholesterol). He randomly selected 9 of his patients and determined their HDL cholesterol. The data is reported in the table below: c) Compute r and r2. Interpret these statistics. d) What is your opinion of the usefulness of using age as a predictor of HDL?
The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 3535 hours and the median is 31.231.2 hours. Twenty-four of the families in the sample turned on the television for 2020 hours or less for the week. The 12th percentile of the data is 2020 hours. Step 1 of 5 : Based on the given information, determine if the following statement is true or false. The 57th percentile is greater than or equal to 3030 hours. True or False?
PrActicE the legalization of marijuana. Among the Democratic voters surveyed, 158 of the 200 people aged 18-29 and 210 of the 300 people aged 50-64 supported legalizing marijuana. Is this difference significant at a = .05? A random sample of individuals in one town was surveyed about their position on

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