# Binomial Variable and Hypothesis Testing

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

Please see the attached file.

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

Answer

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.