A study was conducted to examine the impact of speaking in public on college students. A class of 15 statistics students participated in the study. At the beginning of a lecture the students recorded their systolic blood pressure. During the lecture the instructor called on each student to stand and answer questions about topics in the lecture. After speaking the students once again recorded their blood pressure. The resulting values are given below along with summary statistics. before 107 123 128 125 136 108 130 113 105 136 146 138 108 149 132 after 141 142 146 136 144 111 132 114 103 133 140 130 100 133 113 difference -34 -19 -18 -11 -8 -3 -2 -1 2 3 6 8 8 16 19 before after difference mean 125.6 127.9 -2.267 st dev 14.53 15.45 14.03 Does this information indicate that blood pressure increased because of speaking? Conduct an appropriate hypothesis test and show appropriate steps. Let μ1 mean systolic blood pressure before speaking in public, and μ2 mean systolic blood pressure after speaking in public. The hypothesis for this test are: A. H0: μ1 = μ2 vs. HA: μ1 ≠ μ2 or H0: μd = 0 vs. HA: μd ≠ 0 B. H0: μ1 = μ2 vs. HA: μ1 > μ2 or H0: μd = 0 vs. HA: μd > 0 C. H0: μ1 = μ2 vs. HA: μ1 < μ2 or H0: μd = 0 vs. HA: μd < 0 Fill in the blank: This is a two sample (paired/independent) t-test. The statistic for this test is t = ( ) (to three places after the decimal), and the p-value is ( ) (to three places after the decimal), There (is/is not) sufficient statistical evidence, at the 5% level, to indicate that blood pressure increased because of public speaking.

A study was conducted to examine the impact of speaking in public on college students. A class of 15 statistics students participated in the study. At the beginning of a lecture the students recorded their systolic blood pressure. During the lecture the instructor called on each student to stand and answer questions about topics in the lecture. After speaking the students once again recorded their blood pressure. The resulting values are given below along with summary statistics.

before	107	123	128	125	136	108	130	113	105	136	146	138	108	149	132
after	141	142	146	136	144	111	132	114	103	133	140	130	100	133	113
difference	-34	-19	-18	-11	-8	-3	-2	-1	2	3	6	8	8	16	19

	before	after	difference
mean	125.6	127.9	-2.267
st dev	14.53	15.45	14.03

Does this information indicate that blood pressure increased because of speaking? Conduct an appropriate hypothesis test and show appropriate steps.

Let μ₁ mean systolic blood pressure before speaking in public, and μ₂ mean systolic blood pressure after speaking in public. The hypothesis for this test are:

A. H₀: μ₁ = μ₂ vs. H_A: μ₁ ≠ μ₂ or H₀: μ_d = 0 vs. H_A: μ_d ≠ 0

B. H₀: μ₁ = μ₂ vs. H_A: μ₁ > μ₂ or H₀: μ_d = 0 vs. H_A: μ_d > 0

C. H₀: μ₁ = μ₂ vs. H_A: μ₁ < μ₂ or H₀: μ_d = 0 vs. H_A: μ_d < 0

Fill in the blank: This is a two sample (paired/independent) t-test.
The statistic for this test is t = ( ) (to three places after the decimal),
and the p-value is ( ) (to three places after the decimal),
There (is/is not) sufficient statistical evidence, at the 5% level, to indicate that blood pressure increased because of public speaking.

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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