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Mathematics

1 answer:

wolverine [178]2 years ago

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Answer:

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Step-by-step explanation:

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The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systo

PIT_PIT [208]

Answer:

The estimate is

$52.02 < \mu < 55.78$

Step-by-step explanation:

From the question we are told that

The sample mean is $\ = x = 53.9$

The sample size is n = 24

The standard deviation is $\sigma = 5.6$

Given that the confidence level is 90% the level of significance is mathematically represented as

$\alpha = 100 - 90$

$\alpha = 10 \%$

$\alpha = 0.10$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table.The value is

$Z_{\frac{\alpha }{2} } =Z_{\frac{0.10 }{2} } = 1.645$

The reason we are obtaining critical value 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

NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{ \sqrt{n} }$

substituting values

$E = 1.645 * \frac{5.6 }{ \sqrt{24} }$

$E = 1.880$

The estimate of how much the drug will lower a typical patient's systolic blood pressure(using a 90% confidence level) is mathematically represented as

$\= x - E < \mu < \= x + E$