Homework SourseCan someone please help me with my stats 1 What does it mean
Can someone please help me with my stats.
1. What does it mean to say you have a 95% confidence for an interval?
2. Find the critical value for 94% confidence if the population standard deviation is known. Assume a sample of size n = 15. State postive value with two-decimal accuracy.
3. What does the decision \"fail to reject H0\" mean for a test of hypothesis?
4. Construct a 99% confidence interval for the true proportion p given a sample of n = 180 with x = 120 successes ________,_________?
6. Joe Duh is running for political office. His campaign wants to estimate the proportion of support he has among registered voters. How many voters must be sampled if the campaign wants to have error of no more than 4% with 95% confidence? A local television station has estimated that 48% of registered voters favor his candidacy.
Solution
1.
That means you are 95% confident that the true parameter value is inside your interval.
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2.
As sigma is known, we use z distirbution.
Thus,
alpha/2 = (1 - confidence level)/2 = 0.03
By table/technology,
z(alpha/2) = critical z for the confidence interval = 1.880793608 [ANSWER]
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3.
That means that you are still sticking with the null hypothesis; the sample you have gathered is not enough to prove that the null hypothesis is not true.
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4.
Note that
p^ = point estimate of the population proportion = x / n = 0.666666667
Also, we get the standard error of p, sp:
sp = sqrt[p^ (1 - p^) / n] = 0.035136418
Now, for the critical z,
alpha/2 = 0.005
Thus, z(alpha/2) = 2.575829304
Thus,
Margin of error = z(alpha/2)*sp = 0.090505416
lower bound = p^ - z(alpha/2) * sp = 0.57616125
upper bound = p^ + z(alpha/2) * sp = 0.757172083
Thus, the confidence interval is
( 0.57616125 , 0.757172083 ) [ANSWER]
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