Question

A Brisbane warehouse buys pre-packed bulk bags of Bundaberg Sugar with an advertised mean weight of 20 kilograms. To determine the validity of the advertised claim, the warehouse manager took a random sample of fifty packets from the latest shipment received and found an average weight of the packets of 20.015 kilograms. Bundaberg Sugar know, from analysing data over many years, that their 20kg bulk bag packing process results in a standard deviation of 55 grams.

1. State the direction of the alternative hypothesis used to test the advertised claim. Type the letters gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box.

2. Use the tables in the text to determine the critical value used to conduct the test, assuming a 5% level of significance. If there are two critical values, state only the positive value.

3. Calculate the test statistic, reporting your answer to two decimal places.

4. Is the null hypothesis rejected for this test? Type yes or no.

5. If it is shown later that the "true" average weight of the bags was 20 kilograms as Bundaberg Sugar had claimed, determine the nature of the decision made in the test. Type cd (correct decision), 1 (a Type I error was made) or 2 (a Type II error was made) as appropriate.

6. Regardless of your answer for 4, if the null hypothesis was rejected, would Bundaberg Sugar's advertised claim be valid? Type yes or no.

Answer 1

1:

Here we want to test whether weight is 20 kilograms or not so test should be non directional. Hypotheses are:

2:

The critical values of z for 5% level of significance are -+/- 1.96. Rejection region:

If z < -1.96 or z > 1.96, reject H0

3:

The test statistics is

4:

No since z test statistics does not lie in rejection region.

5;

Since we fail to reject the null hypothesis and it is given that null hypothesis is true so decision is correct. That is no error has been made.

6:

No. In this case conclusion will be "Bundaberg Sugar's advertised claim is not valid.".