Question

The Good Taste ice cream company claims that the amount of ice cream in a container marked 55 ounces is normally distributed with a mean of 54 ounces and a standard deviation of 0.45 ounces. A random sample of 40 ice-cream containers found a sample mean of 53.4 ounces with a sample deviation of 2.45 ounces.
a) Find the 98% confidence interval for the population mean ounces in the ice-cream container. [Round to 4 decimal places.]
b) Does you evidence support the company's claim that the true population weight is 54 ounces? Explain

Answer 1

a)

sample mean, xbar = 53.4
sample standard deviation, s = 2.45
sample size, n = 40
degrees of freedom, df = n - 1 = 39

Given CI level is 98%, hence α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01, tc = t(α/2, df) = 2.426

ME = tc * s/sqrt(n)
ME = 2.426 * 2.45/sqrt(40)
ME = 0.94

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (53.4 - 2.426 * 2.45/sqrt(40) , 53.4 + 2.426 * 2.45/sqrt(40))
CI = (52.4602 , 54.3398)

b)

It does not support the claim because confidenc einterval contains 54

By using Hypothesis

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 54
Alternative Hypothesis, Ha: μ ≠ 54

Rejection Region
This is two tailed test, for α = 0.02 and df = 39
Critical value of t are -2.426 and 2.426.
Hence reject H0 if t < -2.426 or t > 2.426

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (53.4 - 54)/(2.45/sqrt(40))
t = -1.549

P-value Approach
P-value = 0.1295
As P-value >= 0.02, fail to reject null hypothesis.

There is not sufficient evidence to conclude that the true population weight is 54 ounces