Mathematics, 29.07.2020 23:01 alexusdyer94

An article reports that when each football helmet in a random sample of 34 suspension-type helmets was subjected to a certain impact test, 24 showed damage. Let p denote the proportion of all helmets of this type that would show damage tested in the prescribed manner. Required:
a. Calculate a 99% Cl for p.
b. What sample size would be required for the width of a 99% Cl to beat most .10, irrespective of p ?

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Answer from: genyjoannerubiera

0.5043 < p

n = 24

Step-by-step explanation:

From the question we are told that

The sample size is n = 34

The number of damaged helmets is x = 24

Now the proportion of damaged helmets is mathematically represented as

$\r p = \frac{k}{n }$

substituting values

$\r p = \frac{24}{34 }$

$\r p = 0.7059$

Given that the confidence level is 99% the level of significance can be evaluated as

$\alpha = 100 - 99$

$\alpha = 1$ %

$\alpha = 0.01$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table, the value is $Z_{\frac{\alpha }{2} } = 2.58$

The reason we are obtaining critical values of $\frac{\alpha }{2}$ instead of $\alpha$ is because

$\alpha$ represents the area under the normal curve where the confidence level interval ( $1-\alpha$ ) did not cover which include both the left and right tail while

$\frac{\alpha }{2}$ is just the area of one tail which what we required to calculate the margin of error

The margin of error is mathematically represented as

$MOE = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p ( 1 - \r p)}{n} }$

substituting values

$MOE = 2.58 * \sqrt{\frac{ 0.7059 ( 1 - 0.7059)}{34} }$

MOE =0.2016

The 99% confidence interval for p is mathematically represented as

p-MOE < p < p + MOE

substituting values

0.7059 - 0.2016 < p

0.5043 < p

The sample size required for the width of a 99% Cl to beat most 0.10, irrespective of p ? is mathematically represented as

$n \ge \frac{ Z_{\frac{\alpha }{2} } * \sqrt{\r p (1- \r p )} }{\frac{\sigma }{2} }$

Here $\sigma = 0.10$ telling us that the deviation from the sample proportion is set to 0.10 irrespective of the value of $\r p$

so the sample size for this condition is

$n \ge \frac{ 2.58 * \sqrt{ 0.7059 (1- 0.7059)} }{\frac{0.10 }{2} }$

$n \ge 23.51$

=> n = 24

Answer from: Quest

The answer is 26 to 1

Answer from: Quest

median is the value separating the higher half of a data sample, a population or probablity distribution from the lower half.

step-by-step explanation:

say you have 3,8,7,3,1,9,8 order them from lowest to highest

if orderd it would be 1,3,3,7,8,8,9 now you take away from the lowest and the highest until you end up in the middle.

so you would remove the 1 and 9 leaving you with 5 digits remaining

when you've reached the middle that would be your answer so in this case the answer is 7

if there were two numbers left say 7 and 5 you'd and them together so 12 then divide by 2 witch would equal 6 so the answer would be 6

good luck on that project hoped i you at all

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An article reports that when each football helmet in a random sample of 34 suspension-type helmets w...