A coffee manufacturer is interested in whether the mean daily consumption of regular-coffee drinkers is less than that of decaffeinated-coffee drinkers. Assume the population standard deviation for those drinking regular coffee is 1.36 cups per day and 1.46 cups per day for those drinking decaffeinated coffee. A random sample of 52 regular-coffee drinkers showed a mean of 4.53 cups per day. A sample of 48 decaffeinated-coffee drinkers showed a mean of 5.25 cups per day. Use the 0.100 significance level. a. State the null and alternate hypotheses. H0: ?Regular ? ?Decaf H1: ?Regular < ?Decaf H0: ?Regular < ?Decaf H1: ?Regular < ?Decaf H0: ?Regular < ?Decaf H1: ?Regular ? ?Decaf b. Compute the test statistic. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) Test statistic c. Compute the p-value. NOTE: P-value calculators are available through online search. The p-value is d. What is your decision regarding the null hypothesis? Reject H0. Do not reject H0.
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State the null and alternate hypotheses: Null hypothesis (Ho): The mean daily consumption of regular-coffee drinkers is equal to or greater than that of decaffeinated-coffee drinkers. Ho: μRegular ≥ μDecaf Alternate hypothesis (Ha): The mean daily consumption Show more…
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Question 3: A coffee manufacturer is interested in whether the mean daily consumption of regular-coffee drinkers is less than that of decaffeinated-coffee drinkers. A random sample of 50 regular-coffee drinkers showed a mean of 4.35 cups per day. A sample of 40 decaffeinated-coffee drinkers showed a mean of 5.12 cups per day. Assume the population standard deviation for those drinking regular coffee is 1.20 cups per day and 1.36 cups per day for those drinking decaffeinated coffee. Perform an appropriate test at the 1% level of significance. Use the critical value approach. Identify the Case (circle one): μ σ known μ σ unknown p p1 – p2 μ1 – μ2 σ1,σ2 known μ1 – μ2 σ1,σ2 unknown μ1 – μ2 σ1=σ2 unknown
Sri K.
Suppose the coffee industry claimed that the average adult drinks 1.8 cups of coffee per day. To test this claim, a random sample of 50 adults was selected, and their average coffee consumption was found to be 1.9 cups per day. Assume the standard deviation of daily coffee consumption per day is 0.5 cups. Using α=0.10, complete parts a and b below. a. Is the coffee industry's claim supported by this sample? Determine the null and alternative hypotheses. H0: μ = 1.8 H1: μ ≠ 1.8 The z-test statistic is (1.9 - 1.8) / (0.5 / √50). The critical z-score(s) is(are) ±1.645. Because the test statistic (0.1) is less than the critical z-score (-1.645), we reject the null hypothesis. b. Determine the p-value for this test. The p-value is 0.042.
A coffee manufacturer is interested in whether the mean daily consumption of regular coffee drinkers is less than that of decaffeinated-coffee drinkers. A random sample of 50 regular-coffee drinkers showed a mean of 4.35 cups per day, with a standard deviation of 1.20 cups per day. A sample of 40 decaffeinated-coffee drinkers showed a mean of 5.84 cups per day, with a standard deviation of 1.36 cups per day. Use the .01 significance level. Compute the $p$ -value.
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