4. A postmix beverage machine is adjusted to release a certain amount of syrup i

Question

4. A postmix beverage machine is adjusted to release a certain amount of syrup into a chamber where it is mixed with carbonated water. A random sample of 25 beverages was found to have a mean syrup content of 1.05 fluid ounces and a standard deviation of 0.15 fluid ounces. Assume that the syrup content of a beverage is normally distributed (a) Give a point estimate for the mean syrup content in a beverage. Give also the (estimated) error of the estimate. (b) Construct a 95% confidence interval for the mean syrup content. (c) The goal is to have about one ounce of syrup per beverage. Use a critical region to test Ho: H-1 against Hi: Hf1 at a significance level of 5%. (d) Compute the p-value for the test in part 4c.

Explanation / Answer

a)

Pount estimate for mean = 1.05 , error of estimate = s/sqrt(n) = 0.15/sqrt(25) = 0.03

b)

CI for = 95%

n = 25

mean = 1.05

t-value of 95% CI = 2.0639

std. dev. = 0.15

SE = std.dev./sqrt(n)

= 0.15/sqrt(25)

= 0.03000

ME = t*SE

= 2.0639 * 0.03

= 0.06192

Lower Limit = Mean - ME

= 1.05 - 0.06192

= 0.98808

Upper Limit = Mean + ME

= 1.05 + 0.06192

= 1.11192

95% CI (0.9881 , 1.1119 )

c)

critical value for 0.05 = +/- 2.0639

The decision shold be t > 2.0639 or t < -2.0639

Tests stattistics:

t = ( x - mean) / ( s/sqrt(n))

= ( 1.05 - 1) / (0.15/sqrt(25)

= 1.667

we cannot reject the null hypothesis

d) p value = .1085 with df = 24 at 0.05 significance level

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