Question

Tim ran an experiment to test optimum power and time settings for microwave popcorn. His goal was to deliver popcorn with fewer than 10% of the kernels left unpopped, on average. To be sure that the method was successful, he popped 8 more bags of popcorn (selected at random). All were of high quality, with the percentages of unpopped kernels shown: 5.5, 2.4, 7.2, 7.4, 5.1, 10.8, 2.4, 9.2 The appropriate null and alternative hypotheses are: H₀:μ=10H_a:μ<10

(a) Calculate the test statistic. Round your answer to 3 digits after the decimal.

(b) Calculate the P-value. Round your answer to 3 digits after the decimal.

(c) Does this provide evidence that he met his goal of averaging fewer than 10% unpopped kernels? Use 0.05 as the P-value cutoff level. Type "Yes" or "No

Answer 1

Answer)

First we need to find the sample mean and s.d of the given data

Sample mean = 6.25

S.d = 3.0038

N = 8

As the population standard deviation is unknown here we will use t distribution table to conduct the test

Null hypothesis Ho : u = 10

Alternate hypothesis Ha : u < 10

A)

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

t = (6.25 - 10)/(3.0038/√8) = -3.531

B)

Degrees of freedom is = n-1 = 7

For 7 dof and -3.531 test statistics, P-value from t distribution is = 0.004792

C)

As the obtained p-value is less than the given significance 0.1

We reject the null hypothesis Ho

Yes we have enough evidence to conclude that u < 10%