Question

The manager at Coca Cola also claims that less than a quarter of the cans are overfilled. In her sample of 60 cans, she finds that 10 are overfilled. Is there enough evidence that the manager is correct? Test at α = 0.05.

Set up the null and alternate hypotheses.

Compute an appropriate test statistic.

What is the p-value and what do you conclude? Explain.

Answer 1

1) Hypothesis -

H0: p >= 0.25

Ha: p < 0.25 (left tailed)

2) Test statistics -

Sample proportion = 10 / 60 = 0.1667

z = - p / sqrt(p( 1 - p) / n)

= 0.1667 - 0.25 / sqrt(0.25*0.75/60)

= -1.49

This is test statistics value.

3) p-value -

p-value = P( Z < z)

= P( Z < -1.49)

= 1 - P( Z < 1.49)

= 1 - 0.9319

= 0.0681

Since p-value > 0.05 significance level , we do not have sufficient evidence to reject H0.

We conclude at 0.05 significance level that, we fail to support the claim that less than a quarter

of the cans are overfiilled.