2. In a statistical research, population proportion of a particular feature is claimed to be 67%. A researcher doubts this and in order support her claim, she chooses a sample of n=411 from the population and finds out that 300 of them has that particular feature.
(a) (10 pts.) State the appropriate null and alternative hypothesis. (b) (10 pts.) Find test statistics and P-value.
(c) (10 pts.) For α = 0.01 significance level, state your conclusion.
3. (10 pts.) Regarding the standard error of the mean, which of the following is true:
(a) As the sample size decreases, the standard error of the mean decreases. (b) As the sample size increases, the standard error of the mean increases.
(c) Standard error of the mean can be greater than population standard deviation.
(d) As the sample size increases, the standard error of the mean decreases.
4. (10 pts.) As the confidence level of a confidence interval increases, (a) Interval gets narrower.
(b) Sample size increases proportionally.
(c) Interval can be narrowed by increasing sample size sufficiently.
(d) Margin of error decreases.
5. (10 pts.) For a normally distributed data with a mean of μ and a standard deviation of σ, choose the correct one:
(a) P(X < μ) = P( 1-μ < X)
(b) 0.68 < P(μ - σ < X < μ + σ/2)
(c) P(μ - 3σ < X < μ + σ) < 0.83
(d) 0.95 < P(μ - 3σ < X < μ + 2σ)
6. A normally distributed data has a mean of 1550 and a standard deviation of 300.
(a) (10 pts.) Find P (1000 < X < 2000).
(b) (10 pts.) Find the cut-off point for the top 5%
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STA200_O1_Sp20_Online3_TongucCagin_FinalAssessment.docx
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