A buyer for a grocery chain inspects large truckloads of apples to determine the proportion p of apples in the shipment that are rotten. she will only accept the shipment if there is clear evidence that this proportion is less than 0.06 she selects a simple random sample of 200 apples from the over 20000 apples on the truck to test the hypotheses h0: p = 0.06, ha: p < 0.06. the sample contains 9 rotten apples. the p-value of her test is

The p-value of her test is 0.15386.

Step-by-step explanation:

We are given that a buyer for a grocery chain inspects large truckloads of apples to determine the proportion p of apples in the shipment that are rotten.

She selects a simple random sample of 200 apples from the over 20000 apples on the truck and the sample contains 9 rotten apples.

Let p = proportion of of apples in the shipment that are rotten.

SO, Null Hypothesis, : p = 0.06   {means that the proportion of apples in the shipment that are rotten is equal to 0.06}

Alternate Hypothesis, : p < 0.06   {means that the proportion of apples in the shipment that are rotten is less than 0.06}

The test statistics that will be used here is One-sample z proportion statistics;

                               T.S.  =  ~ N(0,1)

where, = proportion of apples that are rotten in a sample of 200 apples =  = 0.045  

           n = sample of apples = 200

So, test statistics  =  

                              =  -1.02

The value of the test statistics is -1.02.

Now, P-value of the test statistics is given by;

        P-value = P(Z < -1.02) = 1 - P(Z 1.02)

                                            = 1 - 0.84614 = 0.15386

Hence, the p-value of her test is 0.15386.

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step-by-step explanation:

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