The Black Fly Beverage Company has just installed a new bottling process that wi

Question

The Black Fly Beverage Company has just installed a new bottling process that will fill 500-mL bottles of its popular margarita beverage. Both overfilling and underfilling bottles are undesirable: Underfilling leads to customer complaints and overfilling costs the company a considerable amount of money. To verify that the filler is set up correctly, the company wants to see whether the mean bottle fill, , is close to the target fill of 500 mL. To this end, a random sample of 36 filled bottles is selected from the output of a test filler run. If the sample results cast a substantial amount of doubt on the hypothesis that the mean bottle fill is the desired 500 mL, the filler’s initial setup will be readjusted.

The bottling company wants to set up a hypothesis test so that the filler will be readjusted if the null hypothesis is rejected. Set up the null and alternative hypotheses for this hypothesis test.

In the context of this situation, interpret making a Type I error; interpret making a Type II error.

Explanation / Answer

here null hypothesis: =500   ( mean filling rate is 500 -ml)

alternate hypotheiss: 500 (mean is not eqaul to 500 ml that is either underfilling or overfilling )

Type I error: rejecting that mean fill is 500 ml when there is no underfilling or overfilling

Type II error: failt to reject that fill is 500 ; when there is underfilling or overfilling

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