18. Given that the variance in the population is unknown and that the sample size is less than 30; which of the following formulas should be used to calculate the sampling distribution of the sample means? A. \( z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}} \) B. \( z=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}} \) C. \( t=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}} \) D. \( t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}} \) 19. What does the Central Limit Theorem say about the mean of the sampling distribution of the sample means? A. It is larger than the population mean. B. It is smaller than the population mean. C. It is equal to the population mean. D. It is equal to the population mean only if the sample is large. 20. In what way does an increase in sample size affect the characteristics of the sampling distribution of the sample mean? A. The sampling distribution is skewed to the right. B. The sampling distribution is skewed to the left. C. The sampling distribution approximates normal distribution. D. The sampling distribution does not change. 21. Rodrigo, a student researcher in Naga City reported in his study that the average annual salary of office clerks in Naga City is PhP93,000 with a standard deviation of PhP19,500. If 45 office clerks are randomly selected, what is the probability that their average annual last page of the test.) A. \( 1.95 \% \) B. \( 19.49 \% \) C. \( 30.51 \% \) D. \( 80.51 \% \) 22. Which is TRUE for both \( t \) - distribution and normal distribution? A. The width of the curve is determined by the mean and the standard deviation of the distribution. B. The t-distribution curve looks more like the normal curve when there is a lower degree of freedom. C. The mean, median, and mode coincide at the center of the distribution. D. The standard deviation of both distributions is determined by the sample size.
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\( z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}} \) B. \( z=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}} \) C. \( t=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}} \) D. \( t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}} \) Show more…
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5- In its standardized form, the normal distribution a- has an area less than 1. b- has a mean of 0 and a standard deviation of 1. c- has a mean of 0 and a variance of 1. d- has an area equal to 0.5. 6- Which of the following about the normal distribution is not true? a- Theoretically, the mean, median, and mode are the same. b- About 2/3 of the observations fall within ±1 standard deviation from the mean. c- Its parameters are the mean, μ and standard deviation, σ. d- It has an area more than 1. 7- The value of the cumulative standardized normal distribution at Z is 0.8770. What is the value of Z ? (Hint: Use the Z table or NORM.S.INV function in excel) a- 0.18. b- 1.47. c- 0.81. d- 1.16. 8- Given that X is a normally distributed variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 46 and 54. (Hint: NORM.S.DIST(-1,TRUE)=0.1587, NORM.S.DIST(1,TRUE)=0.8413, NORM.S.DIST(-2,TRUE)=0.02275 and NORM.S.DIST(2,TRUE)=0.97725) a- 0.97725 b- 0.8413 c- 0.6826 d- 0.9545 9- The standard error of the mean a- is never larger than the standard deviation of the population. b- measures the variability of the mean from sample to sample. c- decreases as the sample size increases. d- All of the above. 10- Suppose the ages of students in Statistics 101 follow a right skewed distribution with a mean of 23 years and a standard deviation of 3 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is incorrect? a- The standard deviation of the sampling distribution is equal to 3 years. b- The mean of the sampling distribution is equal to 23 years. c- The standard error of the sampling distribution is equal to 0.3 years. d- The shape of the sampling distribution is approximately normal. 11- Which of the following statistics is not a measure of central tendency? a- mode b- Q3 c- median d- arithmetic mean. 12- In a perfectly symmetrical distribution, a- the median equals the arithmetic mean. b- the variance equals the standard deviation. c- the interquartile range equals the arithmetic mean. d- the range equals the interquartile range.
Chai S.
The central limit theorem states that when a simple random sample of size n is drawn from any population with mean ? and standard deviation ? , then when n is sufficiently large: A~the distribution of the sample mean is exactly normal B~the standard deviation of the sample mean is ((?2)/n) C~the distribution of the sample mean is approximately normal D~the distribution of the population is exactly normal
Paul F.
4. All random samples of size n = 9 are selected from a normal population with µ = 55 and σ = 10, and the mean is computed for each sample. Then, all the possible samples of size n = 36 are selected from the same population, and the mean is computed for each sample. Which statement below is true? a. The distribution of sample means for samples of n = 9 is less variable than the distribution of sample means for n = 36. b. The distribution of sample means for n = 9 has a smaller mean than the distribution of sample means for n = 36. c. The distribution of sample means for n = 36 has a smaller mean than the distribution of sample means for n = 9. d. The distribution of sample means for samples of n = 36 is less variable than the distribution of sample means for n = 9. 5. An educational specialist develops a new teaching technique for a nutrition course. The educational specialist knows that typically scores on a well-validated measure of nutrition knowledge are normally distributed with µ = 20 and σ = 8. The educational specialist administers their new teaching technique to a sample of n = 25 students who subsequently score M = 22.5 on the measure of nutrition knowledge. Which conclusion can the educational specialist make based on the results of this research study? a. The new teaching technique has an effect on nutrition knowledge because the computed z-score does not reach the z = ±1.96 threshold. b. The new teaching technique does not have an effect on nutrition knowledge because the computed z-score does not reach the z = ±1.96 threshold. c. The new teaching technique has an effect on nutrition knowledge because the computed z-score reaches the z = ±1.96 threshold. d. The new teaching technique does not have an effect on nutrition knowledge because the computed z-score reaches the z = ±1.96 threshold.
Patha S.
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Elementary Statistics a Step by Step Approach
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