Question

Funky pines and inc. is concerned that the 560 mL can of sliced pineapple is being overfilled. The population standard deviation is 1.2 mL. The quality control department took a random sample of 80 cans and found that the arithmetic mean volume was 560.3 mL. At the 5 percent level of significance, can we conclude that the mean volume is greater than 560 mL?

a) Determine the test statistic.
For full marks, your answer should be accurate to 4 decimal places.

z = 0

b)	At the 0.05 significance level, can we conclude that the mean volume is greater than 560 mL? Yes, there is sufficient reason to conclude that the mean volume is greater than 560 mL. No, there is not sufficient reason to conclude that the mean volume is greater than 560 mL.

c) Determine the p-value.
For full marks, your answer should be accurate to 4 decimal places.

p = 0

Answer 1

The provided sample mean is Xˉ=560.3 and the known population standard deviation is σ=1.2, and the sample size is n = 80.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ=560

Ha: μ>560

This corresponds to a right-tailed test, for which a z-test for one mean, with known population standard deviation, will be used.

(2) Rejection Region

Based on the information provided, the significance level is \alpha = 0.05α=0.05, and the critical value for a right-tailed test is

z_c = 1.64

The rejection region for this right-tailed test is

R={z:z>1.64}

(3) Test Statistics

The z-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that

z=2.236>zc​=1.64,

it is then concluded that the null hypothesis is rejected.

Using the P-value approach:

The p-value is p = 0.0127,

and since p = 0.0127<0.05,

it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore,

there is enough evidence to claim that the population mean \muμ is greater than 560, at the 0.05 significance level.

Please like