a) A 95% confidence interval for the mean should be interpreted to mean which of
ID: 3353130 • Letter: A
Question
a) A 95% confidence interval for the mean should be interpreted to mean which of the following? [2] If all possible samples are taken and confidence intervals calculated, 95% of those intervals would include the true population mean somewhere in their interval. You can be 95% confident that you have selected a sample whose interval includes the population mean C Both answers A and B are correct D Neither answer A nor B is correct. b) Which of the following statements is true concerning the width of a confidence interval for a popula- tion proportion? A | The confidence interval is narrower for 99% confidence than for 95% confidence. B The confidence interval is wider for a sample of size 100 than for a sample of size 50. C | The confidence interval is wider for 90% confidence than for 95% confidence. The confidence interval is wider when the sample proportion is 0.50 than when the sample proportion is 0.20. c) A type II error occurs when: 12] A The null hypothesis is incorrectly accepted when it is false B The null hypothesis is incorrectly rejected when it is true C The sample mean differs from the population mean D The test is biased d) Which of the following is not one of the types of variation that is estimated in time-series analysis? [2] Predictable Trend Cyclical Irregular e) The cyclical component of time-series data is usually estimated using: 12] Linear regression analysis Moving averages Exponential smoothing Qualitative methodsExplanation / Answer
a)
The correct answer is option C.
Both answers A and B are correct.
That is if all possible samples are taken and confidence interval estimates are developed, 95%of them would include the true population mean somewhere within their interval.
And we have 95% confidence that we have selected a sample whose interval does include the population mean.
b)
The correct answer is option D.
The confidence interval is wider when the sample proportion is 0.50 than when the sample proportion is 0.20.
Explanation:
The property of Confidence Intervals is:
There is a trade-off between the level of confidence and the precision of the interval. If we want more confidence, we will have to settle for a wider interval.
c)
The correct answer is option A.
The null hypothesis is incorrectly accepted when it is false.
Explanation:
Data appears not statistically significant but actually is, may cause one to reject a valid assessment,
think of this as a “false negative” result.
Fails to reject a false null hypothesis.
The second type of error that can be made in significance testing is failing to reject a false null hypothesis. This kind of error is called a Type II error. Unlike a Type I error, a Type II error is not really an error. When a statistical test is not significant, it means that the data do not provide strong evidence that the null hypothesis is false. Lack of significance does not support the conclusion that the null hypothesis is true. Therefore, a researcher should not make the mistake of incorrectly concluding that the null hypothesis is true when a statistical test was not significant.
Example:
An effective drug is deemed ineffective.
d)
The correct answer is option A.
Predictable.
Explanation:
Traditional methods of time series analysis are concerned with decomposing of a series into a trend, a seasonal variation and other irregular fluctuations.
Different Sources of Variation are
1. Seasonal Variation : Many of the time series data exhibits a seasonal variation which is annual period, such as sales and temperature readings
2. Cyclical Variation: Time series exhibits Cyclical Variations at a fixed period due to some other physical cause, such as daily variation in temperature.
3. Trend Variation: It is a longer term change. Here we take into account the number of observations available and make a subjective assessment of what is long term.
4. Irregular Variation: trend and cyclical variations are removed from a set of time series data, the residual left, which may or may not be random.
e)
The correct answer is option D.
Qualitative methods.
Explanation:
Cyclical variation is a non-seasonal component which varies in recognizable cycle. sometime series exhibits oscillation which do not have a fixed period but are predictable to some extent.
For example, economic data affected by business cycles with a period varying between about 5 and 7 years.
In weekly or monthly data, the cyclical component may describes any regular variation (fluctuations) in time series data. The cyclical variation are periodic in nature and repeat themselves like business cycle, which has four phases (i) Peak (ii) Recession (iii) Trough/Depression (iv) Expansion.
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