Normally, a petri dish nutrient yields a mean culture growth of 22.0 cm2 in the first week. A scientist has invented a new nutrient which she believes will increase the first week growth. She conducts an experiment to test the effectiveness of her new petri dish nutrient formula. Using 25 measurements in her sample, she calculates the sample mean first week growth of 23.5cm2 with a standard deviation of 4.2cm2. (A) State the null and alternative hypotheses for the test. (B) Assuming that the required conditions have been met, what is the value of the test statistic? (C) Is there convincing evidence at the α = 0.05 level that the new petri dish formula effectively increases the first-week growth? Justify your answer.
Normally, a petri dish nutrient yields a mean culture growth of 22.0 cm2 in the first week. A scientist has invented a new nutrient which she believes will increase the first week growth. She conducts an experiment to test the effectiveness of her new petri dish nutrient formula. Using 25 measurements in her sample, she calculates the sample mean first week growth of 23.5cm2 with a standard deviation of 4.2cm2.
(A) State the null and alternative hypotheses for the test.
(B) Assuming that the required conditions have been met, what is the value of the test statistic?
(C) Is there convincing evidence at the α = 0.05 level that the new petri dish formula effectively increases the first-week growth? Justify your answer.
(D) How would the results change if the sample mean were instead 23.4cm2? Comment on what this means about statistical testing.
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