Information about the proportion of a sample that agrees with a certain statement is given below. Use StatKey or other technolog
y to estimate the standard error from a bootstrap distribution generated from the sample. Then use the standard error to give a confidence interval for the proportion of the population to agree with the statement. StatKey tip: Use "CI for Single Proportion" and then "Edit Data" to enter the sample information. Click here to access StatKey. In a random sample of 400 people, 112 agree and 288 disagree. Estimate the standard error using 1000 samples.
1 answer:
Answer:
Answer is given below.
Step-by-step explanation:
Number of people, n = 400
Number of people who agree with the statement is 112.
Number of people who disagree with the statement is 288
Using Stat Key, follow the steps below to obtain the 95% confidence interval for the
proportion of the population to agree with the statement.
1) Open
2) Click on CI for single proportion.
3) Click Edit data key.
4) Enter 112 in count text box.
5) Enter 400 in Sample size text box.
6) Click two-tail.
7) Click Generate 1000 samples key.
Output: (See Image).
Original Sample
Count SampleSize Proportion
112 400 0.280
Bootstrap Sample
Count SampleSize Proportion
128 400 0.320
From the above dot plot , it can be observed that the standard error shows top right corner.
Thus the standard error is 0.022.
From the output, the 95% confidence interval is 0.2371 to 0.325
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Answer:
Step-by-step explanation:
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The objective of this experiment is to test if two different foam-expanding agents have the same foam expansion capacity
Sample 1 (aqueous film forming foam)
n₁= 5
X[bar]₁= 4.7
S₁= 0.6
Sample 2 (alcohol-type concentrates )
n₂= 5
X[bar]₂= 6.8
S₂= 0.8
Both variables have a normal distribution and σ₁²= σ₂²= σ²= ?
The statistic to use to make the estimation and the hypothesis test is the t-statistic for independent samples.:
t=
a) 95% CI
(X[bar]_1 - X[bar]_2) ± *
Sa²= =
= 0.5
Sa= 0.707ç
(4.7-6.9) ± 2.306*
[-4.78; 0.38]
With a 95% confidence level you expect that the interval [-4.78; 0.38] will contain the population mean of the expansion capacity of both agents.
b.
The hypothesis is:
H₀: μ₁ - μ₂= 0
H₁: μ₁ - μ₂≠ 0
α: 0.05
The interval contains the cero, so the decision is to reject the null hypothesis.
<u>Complete question</u>
a. Find a 95% confidence interval on the difference in mean foam expansion of these two agents.
b. Based on the confidence interval, is there evidence to support the claim that there is no difference in mean foam expansion of these two agents?