A pizza company ousted its CEO, who later argued that the quality of pizza had declined since his removal. To test this, a statistician randomly selected 43 volunteers. In a random order, he asked them to eat two slices of pizza created using the old method and two slices of pizza created using the new method. After eating each pair of slices, they were asked to rate the pizza on a scale of 1 to 100. (a) What hypotheses would the statistician test to see if quality had declined since the CEO's removal? H0: xD < 0 vs. Ha: xD = 0H0: pnew - pold = 0 vs. Ha: pnew - pold < 0 H0: The old and new methods are independent vs. Ha: The old and new methods are related H0: ?D = 0 vs. Ha: ?D < 0 H0: ?new - ?old = 0 vs. Ha: ?new - ?old ≠ 0 (b) The average difference in ratings between the pizzas was 8.6 with a standard error of 4.58. What is the value of the test statistic the statistician would find? (3 decimal places) (c) Which conditions does this test meet to ensure its validity? The samples were randomly selected, and the expected number of successes and failures for each was at least 5. The sample was randomly selected, and the sample size is at least 30. The treatments were randomly assigned, and the expected number of participants for each treatment is at least 20. The sample was randomly selected, and np and nq are both at least 15.
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A pizza company ousted its CEO, who later argued that the quality of pizza had declined since his removal. To test this, a statistician randomly selected 43 volunteers. In a random order, he asked them to eat two slices of pizza created using the old method and two slices of pizza created using the new method. After eating each pair of slices, they were asked to rate the pizza on a scale of 1 to 100.
(a) What hypotheses would the statistician test to see if quality had declined since the CEO's removal?
H0: xD < 0 vs. Ha: xD = 0H0: pnew - pold = 0
vs. Ha: pnew - pold < 0 H0: The old and new methods are independent vs. Ha: The old and new methods are related
H0: ?D = 0 vs. Ha: ?D < 0
H0: ?new - ?old = 0 vs. Ha: ?new - ?old ≠ 0
(b) The average difference in ratings between the pizzas was 8.6 with a standard error of 4.58. What is the value of the test statistic the statistician would find? (3 decimal places)
(c) Which conditions does this test meet to ensure its validity?
The samples were randomly selected, and the expected number of successes and failures for each was at least 5.
The sample was randomly selected, and the
The treatments were randomly assigned, and the expected number of participants for each treatment is at least 20.
The sample was randomly selected, and np and nq are both at least 15.
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