Pat ran an experiment to test optimum power and time settings for microwave popc

Question

Pat ran an experiment to test optimum power and time settings for microwave popcorn. His goal was to deliver popcorn with fewer than 8% of the kernels left unpopped on average. He determined that power 9 at 4 minutes was the best combination. To be sure that the method was successful, he popped 8 more bags of popcorn (selected at random) at this setting. All were of high quality with the percentages of unpopped kernels shown below. 4.4, 10.5, 6.3, 2.1, 6.3, 4.2, 7.2, 7.3 Does this provide evidence that he met his goal of an average of fewer than 8% unpopped kernels? Use 0.05 as the P-value cutoff level. Choose the correct null and alternative hypotheses A. H_0: mu notequalto 8 H_A: mu = 8 B. H_0: mu = 8 H_A: mu > 8 C. H_0: mu = 8 H_A: mu 8 H_A: mu = 8 E. H_0: mu = 8 H_A: mu notequalto 8 F. H_0: mu

Explanation / Answer

From the alternative hypothesis this is an left tailed test

also degrees of freedom = n - 1 = 7

So formula of p-value for less than test is

P(t(n - 1) < t) = P(t(n - 1) > - t)

Where t = test statistic value so that -t = -(- 2.20 ) = 2.20

That is we need to find P(t(n - 1) > 2.20)

using excel:

The general formula to find greater than probability of t distribution is "=TDIST(t, df, tails)"

here t =2.20, df =n - 1 = 7, tails = 1

So that P(T > 2.20) = "=TDIST(2.2,7,1)" = 0.031866

After rounding up to four decimal places the p-value is 0.0319   

So that p-value = 0.0319

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