Question

please help me..
need a good explanation

A can-making company claims that the average volume of cans
21.9 cc with a standard deviation of 1.42 cc.
A fresh brewing company suspects that the average volume
the can is less than 21.9 cc. To test it, as many samples were taken
36 cans of drinks, and obtained by the average volume of the beverage cans 21.5
cc.
a) By using a significance level (significant value) of 5%, specify
conclusions drawn from the hypothesis test.
b) Determine p-value for the hypothesis test. If the hypothesis is to be tested
by taking the level of significance (significant value) 5%, specify
conclusions taken

Answer 1

H₀: $\mu$ = 21.9

H₁: $\mu$ < 21.9

The test statistic z = ($\bar x - \mu$)/($\sigma/\sqrt n$)

= (21.5 - 21.9)/(1.42/)

V36

= -1.69

P-value = P(Z < -1.69)

= 0.0455

Since the p-value is less than the significance level (0.0455 < 0.05), so we should reject the null hypothesis.

At 5% significance level there is not sufficient evidence to support the company's claim that the average volume of cans is 21.9 cc.