Paul wants to compare whether the prices of tangerines in two supermarkets differ significantly. He has been noting down the daily prices for the last few days and has found the difference in the sample means to be 20 cents. If the standard deviation of the distribution of the difference between sample means is 28 cents and we are testing the null hypothesis at the 95% confidence level, which statement is true?

Question

Chana Griffith

Mathematics

19 March, 17:14

Paul wants to compare whether the prices of tangerines in two supermarkets differ significantly. He has been noting down the daily prices for the last few days and has found the difference in the sample means to be 20 cents. If the standard deviation of the distribution of the difference between sample means is 28 cents and we are testing the null hypothesis at the 95% confidence level, which statement is true?

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Phoebe Key · Answer 1

We use the simple rules of statistics to accept the null hypothesis

68% of the data falls within 1 sd of the mean95% of the data falls within 2 sd of the mean 99% of the data falls within 3 sd of the mean

20 falls between the range of - 56 to 56 (from the given 95% c. i.), hence we accept the null hypothesis; else, if the mean falls outside the range, we reject the null hypothesis.