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 μg per liter, a typical consumer begins to taste an unpleasant chemical flavor. at α = 0.05, 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?
6.94 7.50 5.87 7.92 8.66 7.78 7.95 6.35 6.16 6.28 5.68 7.02
for the following hypothesis:
a) h0: μ ≤ 6 versus h1: μ > 6, what is the value of the test statistic?
b) what is the p-value?
c) at α = .05, we would
i. reject the null hypothesis.
ii. fail to reject the null hypothesis.

a) 3.52

b)  0.002399

c)  At α = .05 we reject the null hypothesis.

Step-by-step explanation:

We are given the following information:

Population mean, μ = 6 μg per liter

Sample size, n = 12

Alpha, α = 0.05

6.94, 7.50, 5.87, 7.92, 8.66, 7.78, 7.95, 6.35, 6.16, 6.28, 5.68, 7.02

where are data points, is the mean and n is the number of observations.

First, we design the null and the alternate hypothesis

We use One-tailed t test to perform this hypothesis.

a) Formula:

Putting all the values, we have

b) P-value for one tailed t-test at 11 degree of freedom and α = 0.05 is 0.002399

c) Since P-value < 0.05

The result is insignificant.

Thus, at α = .05 we reject the null hypothesis.

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.