Question

At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a mean of 520 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml.

(a) The normal distribution should be used for the sample mean because:________.
1. the sample population has a large mean.
2. the population distribution is known to be normal.
3. the population standard deviation is known.
4. the standard deviation is very small.
(b) Set up hypotheses and a two-tailed decision rule for the correct mean using the 5 percent level of significance.
The hypothesis for a two-tailed decision is:_______.
1.. H0: μ ≠520, H1: μ = 520, reject if z < −1.96 or z > 1.96
2. H0: μ ≠520, H1: μ = 520, reject if z > 1.96 or z < −1.96
3. H0: μ = 520, H1: μ ≠ 520, reject if z > 1.96 or z < −1.96
4. H0: μ =520, H1: μ ≠ 520, reject if z > −1.96 or z < 1.96

Answer 1

A) Population standard deviation is known.

B) Option 3

H0: μ =520,

H1: μ ≠ 520

z > 1.96 or z < -1.96

Explanation:

A) The normal distribution should be used for the sample mean because the population standard deviation is known. Usually, when the standard deviation is unknown we don't use normal distribution except there is an underlying normal approximation.

B) Null Hypothesis:H0: μ =520,

Alternative hypothesis H1: μ ≠ 520

At 5% level of significance, from standard tables, we will reject H0 if;

The test statistic; z > 1.96 or z < -1.96