A deficiency of the trace element selenium in the diet can negatively impact growth, immunity, muscle and neuromuscular function, and fertility. The introduction of selenium supplements to dairy cows is justified when pastures have low selenium levels. Authors of a research paper supplied the following data on milk selenium concentration (mg/L) for a sample of cows given a selenium supplement (the treatment group) and a control sample given no supplement, both initially and after a 9-day period. Initial Measurement Treatment Control 11.4 9.1 9.6 8.7 10.1 9.7 8.5 10.8 10.2 10.9 10.6 10.6 11.9 10.1 9.9 12.3 10.7 8.8 10.2 10.4 10.3 10.9 11.4 10.4 9.3 11.6 10.6 10.9 10.9 8.3 After 9 Days Treatment Control 138.3 9.2 104 8.9 96.4 8.9 89 10.1 88 9.6 103.8 8.6 147.3 10.4 97.1 12.4 172.6 9.2 146.3 9.5 99 8.4 122.3 8.8 103 12.5 117.8 9.1 121.5 93 (a) Use the given data for the treatment group to determine if there is sufficient evidence to conclude that the mean selenium concentration is greater after 9 days of the selenium supplement. (Use ? = 0.05. Use ?d = ?initial − ?9-day.) Find the test statistic. (Round your answer to two decimal places.) t = Find the df. df = Use technology to find the P-value. (Round your answer to four decimal places.) P-value = State your conclusion. Reject H0. We do not have convincing evidence that the mean selenium concentration is greater after 9 days of the selenium supplement.Reject H0. We have convincing evidence that the mean selenium concentration is greater after 9 days of the selenium supplement. Fail to reject H0. We have convincing evidence that the mean selenium concentration is greater after 9 days of the selenium supplement.Fail to reject H0. We do not have convincing evidence that the mean selenium concentration is greater after 9 days of the selenium supplement. (b) Are the data for the cows in the control group (no selenium supplement) consistent with the hypothesis of no significant change in mean selenium concentration over the 9-day period? (Use ? = 0.05. Use ?d = ?initial − ?9-day.) Find the test statistic. (Round your answer to two decimal places.) t = Find the df. df = Use technology to find the P-value. (Round your answer to four decimal places.) P-value = State your conclusion. Fail to reject H0. We do not have convincing evidence that the mean selenium concentration for cows in the control group changed significantly over the 9-day period.Reject H0. We have convincing evidence that the mean selenium concentration for cows in the control group changed significantly over the 9-day period. Fail to reject H0. We have convincing evidence that the mean selenium concentration for cows in the control group changed significantly over the 9-day period.Reject H0. We do not have convincing evidence that the mean selenium concentration for cows in the control group changed significantly over the 9-day period. (c) Would you use the paired t test to determine if there was a significant difference in the initial mean selenium concentration for the control group and the treatment group? Explain why or why not. Yes, the paired t test would be appropriate because the sample differences can be viewed as a random sample from a population of differences, the treatment and control groups were paired samples, and we can assume the sample differences come from a normally distributed population of differences.No, the paired t test would not be appropriate because the number of sample differences is not large enough and the population distribution of differences is positively skewed. Yes, the paired t test would be appropriate since the treatment and control groups were paired samples.No, the paired t test would not be appropriate since the treatment and control groups were not paired samples.

A deficiency of the trace element selenium in the diet can negatively impact growth, immunity, muscle and neuromuscular function, and fertility. The introduction of selenium supplements to dairy cows is justified when pastures have low selenium levels. Authors of a research paper supplied the following data on milk selenium concentration (mg/L) for a sample of cows given a selenium supplement (the treatment group) and a control sample given no supplement, both initially and after a 9-day period. Initial Measurement Treatment Control 11.4 9.1 9.6 8.7 10.1 9.7 8.5 10.8 10.2 10.9 10.6 10.6 11.9 10.1 9.9 12.3 10.7 8.8 10.2 10.4 10.3 10.9 11.4 10.4 9.3 11.6 10.6 10.9 10.9 8.3 After 9 Days Treatment Control 138.3 9.2 104 8.9 96.4 8.9 89 10.1 88 9.6 103.8 8.6 147.3 10.4 97.1 12.4 172.6 9.2 146.3 9.5 99 8.4 122.3 8.8 103 12.5 117.8 9.1 121.5 93 (a) Use the given data for the treatment group to determine if there is sufficient evidence to conclude that the mean selenium concentration is greater after 9 days of the selenium supplement. (Use ? = 0.05. Use ?d = ?initial − ?9-day.) Find the test statistic. (Round your answer to two decimal places.) t = Find the df. df = Use technology to find the P-value. (Round your answer to four decimal places.) P-value = State your conclusion. Reject H0. We do not have convincing evidence that the mean selenium concentration is greater after 9 days of the selenium supplement.Reject H0. We have convincing evidence that the mean selenium concentration is greater after 9 days of the selenium supplement. Fail to reject H0. We have convincing evidence that the mean selenium concentration is greater after 9 days of the selenium supplement.Fail to reject H0. We do not have convincing evidence that the mean selenium concentration is greater after 9 days of the selenium supplement. (b) Are the data for the cows in the control group (no selenium supplement) consistent with the hypothesis of no significant change in mean selenium concentration over the 9-day period? (Use ? = 0.05. Use ?d = ?initial − ?9-day.) Find the test statistic. (Round your answer to two decimal places.) t = Find the df. df = Use technology to find the P-value. (Round your answer to four decimal places.) P-value = State your conclusion. Fail to reject H0. We do not have convincing evidence that the mean selenium concentration for cows in the control group changed significantly over the 9-day period.Reject H0. We have convincing evidence that the mean selenium concentration for cows in the control group changed significantly over the 9-day period. Fail to reject H0. We have convincing evidence that the mean selenium concentration for cows in the control group changed significantly over the 9-day period.Reject H0. We do not have convincing evidence that the mean selenium concentration for cows in the control group changed significantly over the 9-day period. (c) Would you use the paired t test to determine if there was a significant difference in the initial mean selenium concentration for the control group and the treatment group? Explain why or why not. Yes, the paired t test would be appropriate because the sample differences can be viewed as a random sample from a population of differences, the treatment and control groups were paired samples, and we can assume the sample differences come from a normally distributed population of differences.No, the paired t test would not be appropriate because the number of sample differences is not large enough and the population distribution of differences is positively skewed. Yes, the paired t test would be appropriate since the treatment and control groups were paired samples.No, the paired t test would not be appropriate since the treatment and control groups were not paired samples.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Initial Measurement

Treatment	Control
11.4	9.1
9.6	8.7
10.1	9.7
8.5	10.8
10.2	10.9
10.6	10.6
11.9	10.1
9.9	12.3
10.7	8.8
10.2	10.4
10.3	10.9
11.4	10.4
9.3	11.6
10.6	10.9
10.9
8.3

After 9 Days

Treatment	Control
138.3	9.2
104	8.9
96.4	8.9
89	10.1
88	9.6
103.8	8.6
147.3	10.4
97.1	12.4
172.6	9.2
146.3	9.5
99	8.4
122.3	8.8
103	12.5
117.8	9.1
121.5
93

(a)

Use the given data for the treatment group to determine if there is sufficient evidence to conclude that the mean selenium concentration is greater after 9 days of the selenium supplement. (Use ? = 0.05. Use ?_d = ?_initial − ?_9-day.)

Find the test statistic. (Round your answer to two decimal places.)

t =

Find the df.

df =

Use technology to find the P-value. (Round your answer to four decimal places.)

P-value =

State your conclusion.

Reject H₀. We do not have convincing evidence that the mean selenium concentration is greater after 9 days of the selenium supplement.Reject H₀. We have convincing evidence that the mean selenium concentration is greater after 9 days of the selenium supplement. Fail to reject H₀. We have convincing evidence that the mean selenium concentration is greater after 9 days of the selenium supplement.Fail to reject H₀. We do not have convincing evidence that the mean selenium concentration is greater after 9 days of the selenium supplement.

(b)

Are the data for the cows in the control group (no selenium supplement) consistent with the hypothesis of no significant change in mean selenium concentration over the 9-day period? (Use ? = 0.05. Use ?_d = ?_initial − ?_9-day.)

Find the test statistic. (Round your answer to two decimal places.)

t =

Find the df.

df =

Use technology to find the P-value. (Round your answer to four decimal places.)

P-value =

State your conclusion.

Fail to reject H₀. We do not have convincing evidence that the mean selenium concentration for cows in the control group changed significantly over the 9-day period.Reject H₀. We have convincing evidence that the mean selenium concentration for cows in the control group changed significantly over the 9-day period. Fail to reject H₀. We have convincing evidence that the mean selenium concentration for cows in the control group changed significantly over the 9-day period.Reject H₀. We do not have convincing evidence that the mean selenium concentration for cows in the control group changed significantly over the 9-day period.

(c)

Would you use the paired t test to determine if there was a significant difference in the initial mean selenium concentration for the control group and the treatment group? Explain why or why not.

Yes, the paired t test would be appropriate because the sample differences can be viewed as a random sample from a population of differences, the treatment and control groups were paired samples, and we can assume the sample differences come from a normally distributed population of differences.No, the paired t test would not be appropriate because the number of sample differences is not large enough and the population distribution of differences is positively skewed. Yes, the paired t test would be appropriate since the treatment and control groups were paired samples.No, the paired t test would not be appropriate since the treatment and control groups were not paired samples.

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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