Question

In: Statistics and Probability

Find information, preferably pertaining to your major (business) or your interests, and talk about the application...

Find information, preferably pertaining to your major (business) or your interests, and talk about the application of a confidence interval OR a construct a hypothesis test. The application part of this assignment is the most important part so when constructing a confidence interval or a hypothesis test, include how the application can be utilized. Include the actual mathematics behind your choice. Cite your sources correctly.

Solutions

Expert Solution

2)
p^ +- z * sqrt(p^ * (1-p^/n))

X = 784, n = 5000

p^ = X/n = 0.1568, z = 1.96 for 95% CI

Population PROPORTION Confidence Interval
sample size = 5000
sample proportion = 0.1568
confidence level = 95%
Number of Decimals in Results = 4
standard error = 0.005142
Critical z-value = 1.959964
Confidence Interval = 0.1568 +/- 0.0100786280273571
= ( 0.146721371972643, 0.166878628027357)
( 0.1467, 0.1669)
We are 95% confident the true population proportion is between 0.1467 and 0.1669.

3)

Population PROPORTION Hypothesis Test
phat = sample proportion = 0.1568
n = sample size = 5000
α = alpha = 0.1
Step 1: State Ho and Ha
Population parameter comparison value? 0.15
Is this a LEFT, RIGHT or TWO tailed test? RIGHT-tailed
Null Hypothesis: Ho: p ≤ 0.15
Alternate Hypothesis: Ha: p > 0.15
Step 2: State Decision Criteria; Find Critical Values
Reject Ho if z > 1.282
or Reject Ho if p-value < α = 0.1
Step 3: Calculate Test Statistic
Test statistic = z = 1.346600658
p-value = 0.089054441
Step 4: Make Decision
Reject Ho
Reject Ho since p-value (0.0891) IS less than α, alpha, = 0.1.
Also, Reject Ho since the Test statistic (1.3466) meets the rejection criteria in STEP 2.
Step 5: Summarize Decision
There is sufficient statistical evidence to reject Ho.

Please give me a thumbs-up if this helps you out. Thank you! :)


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