Use the following situation to answer questions Vitamin D helps the body absorb calcium and keep bones strong. Human bodies naturally product vitamin D when we are exposed to sunlight. In Alaska, where people have to take supplements for vitamin D due to lack of constant sunshine, a researcher suspects that people who live in Alaska are still vitamin deficient. Normal vitamin D levels in the blood are 20 ng/ml (nanograms per milliliter). 4) The researcher wants to take an SRS of Alaskans and measure the amount of vitamin D in their blood. She suspects a deficiency in the population. Which of the following would be appropriate null and alternative hypotheses? (A) Ho:μ = 20 Hy: a < 20 (B) Ho: <20 HA: = 20 (C) Ho: <20 HA:H>20 (D) Ho: * = 20 HA: > 20 (E) Ho:# <20 HAM = 20 5) A one-sample t-test for a mean at the 010 will be conducted for the
Use the following situation to answer questions Vitamin D helps the body absorb calcium and keep bones strong. Human bodies naturally product vitamin D when we are exposed to sunlight. In Alaska, where people have to take supplements for vitamin D due to lack of constant sunshine, a researcher suspects that people who live in Alaska are still vitamin deficient. Normal vitamin D levels in the blood are 20 ng/ml (nanograms per milliliter). 4) The researcher wants to take an SRS of Alaskans and measure the amount of vitamin D in their blood. She suspects a deficiency in the population. Which of the following would be appropriate null and alternative hypotheses? (A) Ho:μ = 20 Hy: a < 20 (B) Ho: <20 HA: = 20 (C) Ho: <20 HA:H>20 (D) Ho: * = 20 HA: > 20 (E) Ho:# <20 HAM = 20 5) A one-sample t-test for a mean at the 010 will be conducted for the
Use the following situation to answer questions Vitamin D helps the body absorb calcium and keep bones strong. Human bodies naturally product vitamin D when we are exposed to sunlight. In Alaska, where people have to take supplements for vitamin D due to lack of constant sunshine, a researcher suspects that people who live in Alaska are still vitamin deficient. Normal vitamin D levels in the blood are 20 ng/ml (nanograms per milliliter). 4) The researcher wants to take an SRS of Alaskans and measure the amount of vitamin D in their blood. She suspects a deficiency in the population. Which of the following would be appropriate null and alternative hypotheses? (A) Ho:μ = 20 Hy: a < 20 (B) Ho: <20 HA: = 20 (C) Ho: <20 HA:H>20 (D) Ho: * = 20 HA: > 20 (E) Ho:# <20 HAM = 20 5) A one-sample t-test for a mean at the 010 will be conducted for the
Use the following situation to answer questions 4 - 7: Vitamin D helps the body absorb calcium and keep bones strong. Human bodies naturally product vitamin D when we are exposed to sunlight . In Alaska, where people have to take supplements for vitamin D due to lack of constant sunshine, a researcher suspects that people who live in Alaska are still vitamin deficient. Normal vitamin D levels in the blood are 20 ng/ml (nanograms per milliliter). 4) The researcher wants to take an SRS of Alaskans and measure the amount of vitamin D in their blood. She suspects a deficiency in the population. Which of the following would be appropriate null and alternative hypotheses? (A) H:1 = 20 HA: <20 (B) Ho:X<20 HA: = 20 (C) Ho: μ< 20 HA: > 20 (D) H:1 = 20 H:1 > 20 (E) Ho: < 20 HAM = 20 5) A one-sample t-test for a mean at the significance level of a = 0.10 will be conducted for the hypotheses you chose above. For which of the following is the probability of a Type II error the greatest? (A) A sample size of 50 and a true mean value of 15 (B) A sample size of 50 and a true mean value of 18 (C) A sample size of 100 and a true mean value of 15 (D) A sample size of 100 and a true mean value of 18 (E) A sample size of 150 and a true mean value of 18 6) All the conditions for inference were met and the p-value was determined to be 0.08. What is the correct interpretation of p-value? (A) The probability that we get a sample with a mean vitamin D level of ã ng/ml or more extreme when the true mean vitamin D levels in the population are 20 ng/ml is 0.08. (B) The probability that when the significance test is repeated many times, we will be able to reject the null hypothesis that the vitamin D levels in the Alaskan population is 20 ng/ml is 0.08. (C) The probability that we get exactly a mean vitamin D level of & ng/ml when the true mean vitamin D levels in the population are 20 ng/mlis 0.08. (D) The probability of making a Type II error is 0.08. (E) The proportion of significance tests that will correctly reject the null hypothesis of the mean vitamin D levels in the population being equal to 20 ng/ml is 0.08. 7) All the conditions for inference were met and the p-value was determined to be 0.08. Which of the following is the correct conclusions at the 10% significance level? (A) Because our p-value of 0.08 is greater than our significance level, we can reject Ho. We have convincing evidence that the mean vitamin D levels in the Alaskan population is less than 20 ng/ml. (B) Because our p-value of 0.08 is greater than our significance level, we fail to reject Ho. We have convincing evidence that the mean vitamin D levels in the Alaskan population is less than 20 ng/ml. (C) Because our p-value of 0.08 is less than our significance level, we can reject Ho. We have convincing evidence that the mean vitamin D levels in the Alaskan population is less than 20 ng/ml. (D) Because our p-value of 0.08 is less than our significance level, we fail to reject Ho. We have convincing evidence that the mean vitamin D levels in the Alaskan population is less than 20 ng/ml. (E) None of the above gives the correct conclusion about the significance test.
Transcribed Image Text:6) All the conditions for inference were met and the p-value was determined to be 0.08. What is the
correct interpretation of p-value?
(A) The probability that we get a sample with a mean vitamin D level of x ng/ml or more extreme when the true
mean vitamin D levels in the population are 20 ng/ml is 0.08.
(B) The probability that when the significance test is repeated many times, we will be able to reject the null
hypothesis that the vitamin D levels in the Alaskan population is 20 ng/ml is 0.08.
(C) The probability that we get exactly a mean vitamin D level of ng/ml when the true mean vitamin D levels in
the population are 20 ng/ml is 0.08.
(D) The probability of making a Type II error is 0.08.
(E) The proportion of significance tests that will correctly reject the null hypothesis of the mean vitamin D levels in
the population being equal to 20 ng/ml is 0.08.
7) All the conditions for inference were met and the p-value was determined to be 0.08. Which of the
following is the correct conclusions at the 10% significance level?
(A) Because our p-value of 0.08 is greater than our significance level, we can reject Ho. We have convincing
evidence that the mean vitamin D levels in the Alaskan population is less than 20 ng/ml.
(B) Because our p-value of 0.08 is greater than our significance level, we fail to reject Ho. We have convincing
evidence that the mean vitamin D levels in the Alaskan population is less than 20 ng/ml.
(C) Because our p-value of 0.08 is less than our significance level, we can reject Ho. We have convincing evidence
that the mean vitamin D levels in the Alaskan population is less than 20 ng/ml.
(D) Because our p-value of 0.08 is less than our significance level, we fail to reject Ho. We have convincing
evidence that the mean vitamin D levels in the Alaskan population is less than 20 ng/ml.
(E) None of the above gives the correct conclusion about the significance test.
Transcribed Image Text:Use the following situation to answer questions 4-7:
Vitamin D helps the body absorb calcium and keep bones strong. Human bodies naturally product vitamin D
when we are exposed to sunlight. In Alaska, where people have to take supplements for vitamin D due to lack
of constant sunshine, a researcher suspects that people who live in Alaska are still vitamin deficient. Normal
vitamin D levels in the blood are 20 ng/ml (nanograms per milliliter).
4) The researcher wants to take an SRS of Alaskans and measure the amount of vitamin D in their
blood. She suspects a deficiency in the population. Which of the following would be appropriate null and
alternative hypotheses?
(A) Ho:μ = 20
HA:H <20
(B)
Ho: x < 20
HA: * = 20
(C) Ho:μ< 20
Ηλ: μ > 20
(D) Ho: * = 20
HA: 2 > 20
(E) Ho: <20
HA: H = 20
5) A one-sample t-test for a mean at the significance level of a = 0.10 will be conducted for the
hypotheses you chose above. For which of the following is the probability of a Type II error the greatest?
(A) A sample size of 50 and a true mean value of 15
(B) A sample size of 50 and a true mean value of 18
(C) A sample size of 100 and a true mean value of 15
(D) A sample size of 100 and a true mean value of 18
(E) A sample size of 150 and a true mean value of 18
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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