Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 436 gram setting. It is believed that the machine is underfilling the bags. A 28 bag sample had a mean of 433 grams with a standard deviation of 23. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled

Answer 1

There is no sufficient evidence

Explanation:

The hypothesis :

H0 : μ = 436

H1 : μ < 436

Xbar = 433

s = 23

Sample size, n = 28

The test statistic :

(xbar - μ) ÷ (s/√(n))

(433 - 436) ÷ (23/√(28))

-3 ÷ 4.3465914

Test statistic = - 0.690

The Pvalue, calculated from test statistic value, df = n - 1 = 28 - 1 = 27

Pvalue = 0.248

Pvalue > α ; Hence, we fail to reject the null and conclude that there is no sufficient evidence to support the claim that the bags are underfilled