Question

For one binomial experiment, n_{1} = 75 binomial trials
produced r_{1} = 45 successes. For a second independent
binomial experiment, n_{2} = 100 binomial trials produced
r_{2} = 65

successes. At the 5% level of significance, test the claim that the probabilities of success for the two binomial experiments differ.

(a)

Compute the pooled probability of success for the two experiments. (Round your answer to three decimal places.)

(b)

Check Requirements: What distribution does the sample test statistic follow? Explain.

The standard normal. We assume the population distributions are approximately normal.

The Student's *t*. The number of trials is sufficiently
large.

The standard normal. The number of trials is sufficiently large.

The Student's *t*. We assume the population distributions
are approximately normal.

(c)

State the hypotheses.

*H*_{0}: *p*_{1} =
*p*_{2}; *H*_{1}:
*p*_{1} ≠ *p*_{2}

*H*_{0}: *p*_{1} =
*p*_{2}; *H*_{1}:
*p*_{1} <
*p*_{2}

*H*_{0}: *p*_{1} =
*p*_{2}; *H*_{1}:
*p*_{1} > *p*_{2}

*H*_{0}: *p*_{1} <
*p*_{2}; *H*_{1}:
*p*_{1} = *p*_{2}

(d)

Compute p̂_{1} − p̂_{2}.

p̂_{1} − p̂_{2} =

Compute the corresponding sample distribution value. (Test the
difference *p*_{1} − *p*_{2}. Do not
use rounded values. Round your final answer to two decimal
places.)

(e)

Find the *P*-value of the sample test statistic. (Round
your answer to four decimal places.)

(f)

Conclude the test.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(g)

Interpret the results.

Reject the null hypothesis, there is sufficient evidence that the proportion of the probabilities of success for the two binomial experiments differ.

Fail to reject the null hypothesis, there is sufficient evidence that the proportion of the probabilities of success for the two binomial experiments differ.

Fail to reject the null hypothesis, there is insufficient evidence that the probabilities of success for the two binomial experiments differ.

Reject the null hypothesis, there is insufficient evidence that the proportion of the probabilities of success for the two binomial experiments differ.

Answer #1

(a) The pooled probability of success for the two experiments =
**0.629**

(b) The requirements:

The standard normal. The number of trials is sufficiently large.

(c) The hypotheses:

H0: p1 = p2; H1: p1 ≠ p2

(d) p̂1 − p̂2 = **–0.05**

(e) The P-value of the sample test statistic =
**0.4981**

(f) Conclusion: At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(g) Interpretation: Fail to reject the null hypothesis, there is insufficient evidence that the probabilities of success for the two binomial experiments differ.

>> Calculations:

For one binomial experiment, n1 = 75 binomial trials produced r1
= 30 successes. For a second independent binomial experiment, n2 =
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For one binomial experiment,
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experiments. (Round your answer to three decimal places.)
(b) Check Requirements: What distribution does the sample test
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For one binomial experiment,
n1 = 75
binomial trials produced
r1 = 30
successes. For a second independent binomial
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claim that the probabilities of success for the two binomial
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places.)
(b) Check Requirements: What distribution does the
sample test statistic follow? Explain....

For one binomial experiment, n1 = 75 binomial trials
produced r1 = 45 successes. For a second independent
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experiments. (Round your answer to three decimal places.)
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