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musickatia [10]
3 years ago
6

in a given year, the rate of flu infection for the general public was 8.3%. And sample of 200 people who receive the flu vaccine

, the rate of flu infection was just 3.5%. What conclusion should you draw?​

Mathematics
1 answer:
makkiz [27]3 years ago
5 0

Answer:

\fbox{\begin{minipage}{10em}Option A is correct\end{minipage}}

Step-by-step explanation:

<em>Step 1: Define significance level</em>

In this hypothesis testing problem, significance levels α is selected: 0.05, the associated z-value from Laplace table:

Φ(z) = α - 0.5 = 0.05 - 0.5 = -0.45

=> z = -1.645

<em>Step 2: Define null hypothesis (</em>H_{0}<em>) and alternative hypothesis (</em>H_{1}<em>)</em>

H_{0} : rate of flu infection p = 8.3% or 8.3/100 = 0.083

H_{1} : rate of flu infection p < 8.3% or 8.3/100 = 0.083

<em>Step 3: Apply the formula to check test statistic:</em>

K = \frac{f - p}{\sqrt{p(1 - p)} } * \sqrt{n}

with f is actual sampling percent, p is rate of flu infection of H_{0}, n is number of samples.

The null hypothesis will be rejected if K < z

<em>Step 4: Calculate the value of K and compare with </em>z

K = \frac{(\frac{3.5}{100})  - 0.083}{\sqrt{0.083(1 - 0.083)} } * \sqrt{200} = -2.46  

We have -2.46 < -1.645

=>This is good evidence to reject null hypothesis.

=> The actual rate is lower. (As H_{1} states)

Hope this helps!

:)

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