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The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean μ = 125 and standard deviation σ = 14. Systolic blood pressure for males follows a normal distribution. Calculate the z-scores for the male systolic blood pressures 100 and 150 millimeters.

For 100mm blood pressure, z =( x-µ)/σ = (100-125)/14 = -1.7857

For 150mm blood pressure, z =( x-µ)/σ = (150-125)/14 = 1.7857

You perform a one-sample t test and calculate a t statistic of 3.0. The mean of your sample was 1.3 and the standard deviation was 2.6. How many participants were used in this study?

[pic]

Men have an average weight of 172 pounds with a standard deviation of 29 pounds. Find the probability that 20 randomly selected men will have a sum weight greater than 3600 pounds.

Average weight µ = 172 pounds

Sample size = 20

Sample standard deviation = 29/√20 =6.485

X = 3600/20 = 180

We will use t-distribution here as sample size is 20, which is less than 30.

Hence, t = (180-172)/6.485 = 1.233

Degree of freedom = 20 – 1 = 19

Hence, P(X>180) = P(t>1.233) =0.1163 (noted from t-distribution tables)

Hence, probability that sum will be greater than 3600 pounds is 0.1163.

The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population.

a. Is this a test of one mean or proportion?

proportion

b. State the null and alternative hypotheses using symbols.

Ho: p = 0.095

H1: p < 0.095

c. Is this a right-tailed, left-tailed, or two-tailed test?

Left tailed

d. What symbol represents the random variable for this test?

[pic]

e. In words, define the random variable for this test.

the proportion of people in that town surveyed suffering from depression.

f. Calculate the following:

i. x

x = 7

ii. n

n=100

iii. p′

p’=0.07

g. Calculate σx

Standard error σx = [pic]

h. State the distribution to use for the hypothesis test.

Normal

i. Find the p-value.

[pic]

p-value = P(z ................
................

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