chad randomly chooses a card from a standard deck 30 times. what is the probability he gets a diamond exactly 4 times
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Answer:
The p-value of the test is 0.0764 > 0.05, which means that there is not enough evidence to reject the null hypothesis that the proportion is of at most 0.009, and thus we can conclude that the supplier has met the guarantee.
Step-by-step explanation:
Your overseas supplier of engines guarantees that no more than 0.9% of the new engines shipped to you will fail a simple electrical test.
At the null hypothesis, we test if the proportion is of at most 0.9% = 0.009, that is:
At the alternative hypothesis, we test if the proportion is of more than 0.009, that is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
0.009 is tested at the null hypothesis:
This means that
50 of these engines, and you find that 1 is defective.
This means that
Value of the test statistic:
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion above 0.02, which is 1 subtracted by the p-value of z = 1.43.
Looking at the z-table, z = 1.43 has a p-value of 0.9236.
1 - 0.9236 = 0.0764.
The p-value of the test is 0.0764 > 0.05, which means that there is not enough evidence to reject the null hypothesis that the proportion is of at most 0.009, and thus we can conclude that the supplier has met the guarantee.