# 4. A manufacturer packs a prize in each box ofits cereal and claims that the probabilities ofgetting various prizes are as follows:Probability0.20PrizeRingKey ChainPuzzle0.300.15Pen0.25Flashlight0.10To see if the company's claim is accurate, aconsumer group randomly selects 1,020 boxes ofthis product and obtains the following data:PrizeFrequency186RingKey ChainPuzzle327168Pen225Flashlight114Using a 5% level of significance, test the claimthat the distribution of prizes is what themanufacturer claims.

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Step 1

It is given that the probabilities of getting various prizes.

Step 2

In this case, the chi-square goodness of fit test is appropriate.

The null and alternative hypotheses are shown below:

H0: The true proportions of all 5 categories is equal to their expected value.

H1: At least one proportions is different from its expected value.

The test statistic is obtained as follows:

Step 3

Here, Oi represents observed values and Ei represents frequencies.

The ex...

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