Christine recently switched her primary doctor to one specializing in caring for elderly patients. On her new doctor's website, it says that the mean systolic blood pressure among elderly females is 115 millimeters of mercury (mmHg). Christine believes the value is actually higher. She bases her belief on a recently reported study of 14 randomly selected, elderly females. The sample mean systolic blood pressure was 130 mmHg, and the sample standard deviation was 24 mmHg. Assume that the systolic blood pressures of elderly females are approximately normally distributed. Based on the study, at the 0.05 level of significance, can it be concluded that μ, the population mean systolic blood pressure among elderly females, is greater than 115 mmHg? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. A. Find the value of the test statistic and round to 3 or more decimal places. (I have posted a picture of an example problem and the equation to use, with the correct answer as every expert I have asked thus far has gotten this problem wrong.) B. Find the critical value. (Round to three or more decimal places.) C. Can it be concluded that the mean systolic blood pressure among elderly females is greater than 115mm Hg?

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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Christine recently switched her primary doctor to one specializing in caring for elderly patients. On her new doctor's website, it says that the mean systolic blood pressure among elderly females is 115 millimeters of mercury (mmHg). Christine believes the value is actually higher. She bases her belief on a recently reported study of 14 randomly selected, elderly females. The sample mean systolic blood pressure was 130 mmHg, and the sample standard deviation was 24 mmHg. Assume that the systolic blood pressures of elderly females are approximately normally distributed. Based on the study, at the 0.05 level of significance, can it be concluded that μ, the population mean systolic blood pressure among elderly females, is greater than 115 mmHg? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places.

A. Find the value of the test statistic and round to 3 or more decimal places. (I have posted a picture of an example problem and the equation to use, with the correct answer as every expert I have asked thus far has gotten this problem wrong.)

B. Find the critical value. (Round to three or more decimal places.)

C. Can it be concluded that the mean systolic blood pressure among elderly females is greater than 115mm Hg?

(c) Finding the value of the test statistic
Since we're assuming the null is true, we use μ = 36. We also have that x = 32, s = 11, and n = 14. So we get the following.
32-36
11
✓√14
t
x-μ
S
√n
≈ 1.361

The Journal de Botanique reported that the mean height of Begonias grown while being treated with a
particular nutrient is 36 centimeters. To check whether this is still accurate, heights are measured for a
random sample of 14 Begonias grown while being treated with the nutrient. The sample mean and sample
standard deviation of those height measurements are 32 centimeters and 11 centimeters, respectively.
Assume that the heights of treated Begonias are approximately normally distributed. Based on the sample,
can it be concluded that the population mean height of treated begonias, µ, is different from that reported in
the journal? Use the 0.10 level of significance. Perform a two-tailed test. Then complete the parts below. Carry
your intermediate computations to three or more decimal places.
MATL
BU
Ch

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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