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Problem #2 Nike claims that golfers can lower their scores by using their newly designed golf clubs. Eight golfers are randomly selected and each is asked to give his or her most recent score. After using the new clubs for one month, the golfers are again asked to give their most recent scores. (Assume for this problem that golfers will tell the truth!) The scores for each golfer are given in the table below. Assuming the golf scores are normally distributed, is there enough evidence to support Nike's claim at a = 0.05? Golfer 1 2 4 5 6 7 Score 89 84 82 92 85 (Old Design) Score (New Design) 82 83 3 96 92 84 74 76 | 91 80 |8|9 91 | 91

Problem #2 Nike claims that golfers can lower their scores by using their newly designed golf clubs. Eight golfers are randomly selected and each is asked to give his or her most recent score. After using the new clubs for one month, the golfers are again asked to give their most recent scores. (Assume for this problem that golfers will tell the truth!) The scores for each golfer are given in the table below. Assuming the golf scores are normally distributed, is there enough evidence to support Nike's claim at a = 0.05? Golfer 1 2 4 5 6 7 Score 89 84 82 92 85 (Old Design) Score (New Design) 82 83 3 96 92 84 74 76 | 91 80 |8|9 91 | 91

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HYPOTHESIS TESTING FOR A POPULATION CORRELATION COEFFICIENT Remember your symbols: r= Sample correlation Coefficient Hypotheses, Degrees of Freedom, and the Test Statistic Hypotheses: While you CAN use left, right, and two-tailed hypotheses for the population. correlation coefficient, we will ONLY consider two-tailed hypothesis tests for p. Degrees of Freedom: A t-test will be used to test whether the correlation between two variables is significant. The degrees of freedom for hypothesis testing for the population correlation coefficient will be d.f. = n-2 (where n is the number of pairs of data) Test Statistic: We use the test statistic r (the sample correlation coefficient) Advertising expenses (1000s of $) USE THE TI-84 LinRegTTest to find your t-test statistic and your p-value Complete the following steps. Identify each step with the appropriate corresponding number. 1. Write the claim and the null and the alternate hypotheses. 2. Identify a. 3. Draw a distribution to represent it and identify the critical value(s). 4. Write the inequality that identifies the rejection area(s). 5. Find the test statistic. 6. Make a decision about your test. 7. Write a sentence describing your decision about the claim in context with the problem. 2.4 1.6 2.0 2.6 1.4 1.6 2.0 2.2 EXAMPLE 1 Is there enough evidence at a = 0.01 to conclude that there is a significant statistical correlation between advertising hours and company sales? Company Sales (1000s of $) p= population correlation 225 184 220 240 180 184 186 215 3 41 Ryect Ho if + test 5 Coefficent Claim There is a statistical Correlation between advertising hours and company sales. Ho: P = O H₁: P = 3,707 or t-test ≤-3707 r=01913 t=5,478 P-value 0.00155 6 Ryect. Ho IN t=-3707 m +=3,707 There is evidence at a =, 01 to support the claim that there is a significent Correlation between advertising sales and company sales.
Transcribed Image Text:HYPOTHESIS TESTING FOR A POPULATION CORRELATION COEFFICIENT Remember your symbols: r= Sample correlation Coefficient Hypotheses, Degrees of Freedom, and the Test Statistic Hypotheses: While you CAN use left, right, and two-tailed hypotheses for the population. correlation coefficient, we will ONLY consider two-tailed hypothesis tests for p. Degrees of Freedom: A t-test will be used to test whether the correlation between two variables is significant. The degrees of freedom for hypothesis testing for the population correlation coefficient will be d.f. = n-2 (where n is the number of pairs of data) Test Statistic: We use the test statistic r (the sample correlation coefficient) Advertising expenses (1000s of $) USE THE TI-84 LinRegTTest to find your t-test statistic and your p-value Complete the following steps. Identify each step with the appropriate corresponding number. 1. Write the claim and the null and the alternate hypotheses. 2. Identify a. 3. Draw a distribution to represent it and identify the critical value(s). 4. Write the inequality that identifies the rejection area(s). 5. Find the test statistic. 6. Make a decision about your test. 7. Write a sentence describing your decision about the claim in context with the problem. 2.4 1.6 2.0 2.6 1.4 1.6 2.0 2.2 EXAMPLE 1 Is there enough evidence at a = 0.01 to conclude that there is a significant statistical correlation between advertising hours and company sales? Company Sales (1000s of $) p= population correlation 225 184 220 240 180 184 186 215 3 41 Ryect Ho if + test 5 Coefficent Claim There is a statistical Correlation between advertising hours and company sales. Ho: P = O H₁: P = 3,707 or t-test ≤-3707 r=01913 t=5,478 P-value 0.00155 6 Ryect. Ho IN t=-3707 m +=3,707 There is evidence at a =, 01 to support the claim that there is a significent Correlation between advertising sales and company sales.
**For each of the following, complete the steps listed below. Identify and write each step with the appropriate corresponding number. 1. Write the claim and the null and the alternate hypotheses with proper notation. 2. Identify the level of significance. 3. Draw a distribution to represent it and identify the critical value. 4. Write the inequality that identifies the rejection area(s). 5. USE YOUR CALCULATOR to find the t-test statistic and the p-value. 6. Make a decision about your test. 7. Write a sentence describing your decision about the claim. Problem #2 Nike claims that golfers can lower their scores by using their newly designed golf clubs. Eight golfers are randomly selected and each is asked to give his or her most recent score. After using the new clubs for one month, the golfers are again asked to give their most recent scores. (Assume for this problem that golfers will tell the truth!) The scores for each golfer are given in the table below. Assuming the golf scores are normally distributed, is there enough evidence to support Nike's claim at a = 0.05? Golfer 1 2 4 5 6 7 Score 89 84 82 74 92 85 (Old Design) Score (New Design) 82 83 3 96 92 84 76 91 80 8 91 91
Transcribed Image Text:**For each of the following, complete the steps listed below. Identify and write each step with the appropriate corresponding number. 1. Write the claim and the null and the alternate hypotheses with proper notation. 2. Identify the level of significance. 3. Draw a distribution to represent it and identify the critical value. 4. Write the inequality that identifies the rejection area(s). 5. USE YOUR CALCULATOR to find the t-test statistic and the p-value. 6. Make a decision about your test. 7. Write a sentence describing your decision about the claim. Problem #2 Nike claims that golfers can lower their scores by using their newly designed golf clubs. Eight golfers are randomly selected and each is asked to give his or her most recent score. After using the new clubs for one month, the golfers are again asked to give their most recent scores. (Assume for this problem that golfers will tell the truth!) The scores for each golfer are given in the table below. Assuming the golf scores are normally distributed, is there enough evidence to support Nike's claim at a = 0.05? Golfer 1 2 4 5 6 7 Score 89 84 82 74 92 85 (Old Design) Score (New Design) 82 83 3 96 92 84 76 91 80 8 91 91
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