Question

# Medical researchers think that p = 0.70 is the proportion of all teenagers with high blood...

Medical researchers think that p = 0.70 is the proportion of all teenagers with high blood pressure whose blood pressure would decrease if they took calcium supplements. To test this theory, the researchers plan a clinical trial (experiment) in which n = 200 teenagers with high blood pressure will take regular calcium supplements.

In the clinical trial, 156 of the 200 teenagers taking calcium supplements experienced a decrease in blood pressure. Find the probability that if another clinical trial were to be performed with n = 200 teenagers, the sample proportion that would experience a decrease in blood pressure will be higher than 0.78.
a. 0.005842
b. 0.010614
c. 0.002004
d. 0.006772
e. 0.008125

Solution

Given that,

p = 0.70

1 - p = 1 - 0.70 = 0.30

n = 200  = p = 0.70  = [p( 1 - p ) / n] = [(0.70 * 0.30) / 200 ] = 0.0324

P( > 0.78) = 1 - P( < 0.78)

= 1 - P(( -  ) /  < (0.78 - 0.70) / 0.0324)

= 1 - P(z < 2.47 )

Using z table

= 1 - 0.993228

= 0.006772

correct option is = d

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