Researchers have conducted a survey of 1600 coffee drinkers asking how much coffee they drink in order to confirm previous studies. Previous studies have indicated that 72% of Americans drink coffee. The results of previous studies (left) and the survey (right) are below. Response | Observed O | Expected E | (O - E)² --- | --- | --- | --- 2 cups per week | 206 | 240 | 1156 1 cup per week | 193 | 208 | 225 1 cup per day | 462 | 432 | 900 2+ cups per day | 739 | 720 | 361 Is there enough evidence to conclude that the distributions are the same at ? = 0.10? a. there is no enough statistical evidence to reject H?. b. there is no enough statistical evidence to accept H?. c. non of them d. there is enough statistical evidence to reject H?.
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Step 1: Calculate the chi-square value for each category using the formula: \(\chi^2 = \frac{(O - E)^2}{E}\), where O is the observed value and E is the expected value. Show more…
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Researchers have conducted a survey of 1600 coffee drinkers asking how much coffee they drink in order to confirm previous studies. Previous studies have indicated that 72% of Americans drink coffee. The results of previous studies (left) and the survey (right) are below: Observed Expected (O - E)^2 Response O E 2 cups per week 206 240 1156 1 cup per week 193 208 225 1 cup per day 462 432 900 2+ cups per day 739 720 361 Calculate the test statistic at Α = 0.10. a. -8.4831 b. non of them c. 9.4831 d. 8.4831 e. -9.4831
Federico C.
Researchers have conducted a survey of 600 coffee drinkers asking how much coffee they drink in order to confirm previous studies. Previous studies have indicated that 72% of Americans drink coffee. The results of previous studies (left) and the survey (right) are below. At a = 0.05, is there enough evidence to conclude that the distributions are the same? % of Coffee Drinkers Response Frequency 2 cups per week 150 1 cup per week 193 1 cup per day 162 2+ cups per day 95 State the null and alternative hypotheses: Null hypothesis: The distributions of coffee drinkers are the same. Alternative hypothesis: The distributions of coffee drinkers are different. b. Fill in the table and use the chi-square formula to calculate the chi-square statistic: Response % of E-0 (E = 0)? (E = 0)?/E Coffee Drinkers 2 cups per week 150 120 0.8 1 cup per week 193 216 1.12 1 cup per day 162 180 1.11 2+ cups per day 95 84 0.88 Write the chi-square formula here: Chi-square = Σ((O - E)^2 / E) Show your calculation of the statistic here: Chi-square = ((150-120)^2 / 120) + ((193-216)^2 / 216) + ((162-180)^2 / 180) + ((95-84)^2 / 84) = (900/120) + (529/216) + (324/180) + (121/84) = 7.5 + 2.45 + 1.8 + 1.44 = 13.19 Use the gchisq function in R to find the p-value of your test statistic. Copy and paste your code and response here: Code: p_value <- 1 - pchisq(13.19, df = 3) p_value Response: The p-value of the test statistic is 0.004. Write conclusion in complete sentences for your test: Based on the chi-square test with a significance level of 0.05, there is enough evidence to conclude that the distributions of coffee drinkers are different.
Dominador T.
National Coffee Drinking Trends is "the publication" in the coffee industry. Each year it tracks consumption patterns in a wide variety of situations and categories and has done so for over five decades. A recent edition says that $39 \%$ of the total coffee drinkers age 18 years and over have purchased shade-grown coffee in the last year. If this percentage is true for coffee drinkers at Crimson Light's coffeehouse, what is the probability that of the next 50 customers purchasing coffee at Crimson Light's, a. more than 20 will ask for a shade-grown variety? b. fewer than 15 will ask for a shade-grown variety?
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