Question

A manufacturer of chocolate chips would like to know whether it’s 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 under filled?

There is not sufficient evidence to support the claim that the bags are under filled.

Or

There is sufficient evidence to support the claim that the bags are under filled.

Answer 1

The null hypothesis H₀ : There is not sufficient evidence to support the claim that the bags are under filled. [mean>=436]

Alternative hypothesis H₁ : There is sufficient evidence to support the claim that the bags are under filled. [mean<436]

The desired quantity to be filled in each bag is supposed to be = 436 g

According to the data, the machines are underfilling the bags.

From the sample data, the mean = 433 g

Standard deviation = 23

Assuming the population distribution is approximately normal, a left tailed test is performed.

Now, testing population mean, with the above data,

x-bar=433 ,

s=23,

n=28,

From the z value, the graph is as shown:

From the 'cumulative normal distribution table', the p-value can be found.

Table is as shown here.

According to another simulator, the p-value is generated as shown above. This is only to prove that the calculations done are correct.

The P-value is the probability that the data would be at least this inconsistent with the hypothesis, assuming the hypothesis is true.

For null hypotheses [mean>=436], the p-value=0.2480.

A level of significance of 0.05 is used. Hence alpha=0.05.

Now since p-value=0.2480 , p-value is not < alpha.

Null hypothesis is thus not rejected.

Hence, there is no sufficient evidence to support the claim that the bags are under filled.