I need to check my answer to this one

Beer shelf life is a problem for brewers and distributors because when beer is stored at room temperature, its flavor deteriorates. When the average furfuryl ether content reaches 6 g per liter, a typical consumer begins to taste an unpleasant chemical flavor. At = .05, would the following sample of 12 randomly chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold?

5.72 5.46 5.91 7.73 6.26 5.33 8.86 7.52 5.80 8.97 5.31 7.61

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(a) For the following hypothesis

H0: 6 versus H1: > 6, what is the value of the test statistic? (Round your answer to 3 decimal places.)

Test statistic

(b) What is the p-value? (Round your answer to 4 decimal places.)

p-value

(c) At = .05, we would

multiple choice

reject the null hypothesis.

fail to reject the null hypothesis.