Campbell's is considering making an unadvertised change in one of its soups. They select 25 people and , using a double blind taste test, have each one of the 25 people taste both the original version of the soup and the new version. Each person is then asked to rate both versions of the soup.
Using a 95% confidence interval, the null hypothesis that there is no difference in the two versions of the soup is tested. This test is a paired t test, with 24 degrees of freedom. The calculated confidence interval is (2.00, 4.00), with a calculated t value of 3.00. The researcher who reports the results states, "We failed to reject the null hypothesis of no difference in the two versions of the soup because the calculated t statistic (3.00) is contained within the calculated confidence interval."
Critique this researcher's explanation.
2007-01-30 06:45:35 · 3 answers · asked by stuck 1 in Science & Mathematics ➔ Mathematics
I think that the approach is incorrect.
The t value should not be used to compare with the confidence interval.
The confidence interval and level are used to tell how confident you are to show the number will fall between you confidence level.
2007-01-30 07:31:46 · update #1
The researcher made a serious error. The null hypothesis states that there is no difference in the two versions, meaning that the mean difference between the ratings of the two soups is zero. You should be looking to see if 0 is in the confidence interval, not 3. Since 0 is not in the confidence interval, you would reject the null hypothesis at the 5% significance level.
2007-01-30 07:37:56 · answer #1 · answered by blahb31 6 · 0⤊ 0⤋
2 sided alt hypothesis ability you have 2 z scores z? ? = .10. ability the two cutoffs make 2 rejection areas with a community=.10 This leaves .ninety for the do no longer reject section. chop up that for the period of two and each and each section is .40 5 or .4500 utilising a table of z scores for useful factors: z=+/- a million.sixty 5 or determination C c) |Z| ? a million.ninety six (that is yet in a distinctive way of writing Z ? -a million.ninety six and Z ? a million.ninety six)
2016-11-01 21:52:19 · answer #2 · answered by Anonymous · 0⤊ 0⤋
I could answer that but I don't think that that would help your understanding.
What do you think of the researcher's explanation? I'd be glad to critique your critique!
2007-01-30 07:19:18 · answer #3 · answered by modulo_function 7 · 0⤊ 0⤋