Answer Question 10: The pulse rates of women are normally distributed with a sta

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Answer Question 10:

The pulse rates of women are normally distributed with a standard deviation of 12.5 beats per minute. A medical group samples the pulse rates of 100 women they see during one day and find their mean to be 74.4 with a standard deviation of 11.7 beats per minute. Use a 0.05 significance level to test the claim that the sample does come from a population with mean equal to 74 beats per minute. Use the P-value method of hypothesis testing. A coin is tossed 15 times. A person who claims to have the ability to predict whether the coin will land heads is asked to predict the outcome of each toss. She correctly predicts 10 of the 15 tosses. a. Find the probability of her correctly predicting 10 or more tosses if she randomly guesses on these tosses by using the Normal Approximation, be sure to state why it is permissible to use this Normal Approximation. A research group polls 764 randomly selected adults, and asked them if they would like someone like Homer Simpson to be their neighbor. 589 said no. a. Construct a 94% confidence interval of the percentage of all adults who do not want Homer Simpson to be their neighbor. b. Is it correct for a newspaper headline to read: "80% of people do not want to live next to Simpson"? Explain your reasoning. c. How many people need to be surveyed if you want 98% confidence that the margin of error is two percentage points?

Explanation / Answer

1) Hypothesis:
Ho : mu = 74
Ha: mu not equal to 74

Data:
x = 74.4 , s = 12.5 , n =100

Test statistic :

t = ( x - mean) / ( s/sqrt(n))
= (74.4 - 74) / ( 12.5 / sqrt(100))
= 0.32
p value is calculated using t = 0.32 , df = 99

P value = .749643.

Here, we fail to reject the null hypothesis.

3)
p = 589 / 764 = 0.771

a) z value at 94% CI = 1.88

CI = p +/- z * sqrt( p * ( 1-p)/n)
= 0.771 +/- 1.88 * sqrt( 0.771 * 0.229/ 764)
= (0.74242 , 0.79958)
b)

z value at 98% CI = 2.33 ,ME = 0.02
ME = z * sqrt( p * ( 1-p)/n)
0.02 = 2.33 * sqrt ( 0.771 * 0.229/n)
n = 2396.303
n = 2396

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