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# Binomial Variable and Hypothesis Testing

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Using the accompanying probability distribution, find the following values
X P(x)
1 .25
2 .27
3 .05
4 .43

a) Mean
b) Standard Deviation

Assume that the cure rate for a certain drug is 20% and that 15 patients are tested with this drug. Find the following:
a) Mean
b) Standard Deviation
c) P (exactly 4 cures)
d) P (exactly 4 cures)

A snack company distributes chips in bags labeled 6 ounces. The local Bureau of Weights and Measures randomly selects 50 bags of chips and obtains a sample mean of 5.9 ounces. Assuming that the standard deviation is known to be 0.8, test the claim at the .05 significance level that the bags contain less than 6 ounces. Identify the following:

a) The Null Hypothesis
b) Critical Value
c) Test Statistics
d) Your Conclusion regarding the Null Hypothesis
e) Your Statement regarding the claim.

https://brainmass.com/statistics/hypothesis-testing/binomial-variable-hypothesis-testing-108751

#### Solution Preview

Statistics
________________________________________
Using the accompanying probability distribution, find the following values
X P(x)
1 .25
2 .27
3 .05
4 .43

a) Mean
b) Standard Deviation

X P(X) x.P(X) x2.P(X)
1 0.25 0.25 0.25
2 0.27 0.54 1.08
3 0.05 0.15 0.45
4 0.43 1.72 6.88
Total 1 2.66 8.66

Mean =
Variance =V(x)=
Standard Deviation =

Assume that the cure rate for a certain drug is 20% and ...

#### Solution Summary

Calculation of Binomial variable and students t test with Null Hypothesis, Alternative Hypothesis, Significance Level, Critical Value, P value. The interpretation of results is also given.

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