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Bogdan [553]
3 years ago
14

An epidemiologist is worried about the prevalence of the flu in East Vancouver and the potential shortage of vaccines for the ar

ea. She will need to provide a recommendation for how to allocate the vaccines appropriately across the city. She takes a simple random sample of 333 people living in East Vancouver and finds that 40 have recently had the flu.
The epidemiologist will recommend East Vancouver as a location for one of the vaccination programs if her sample data provide sufficient evidence to support that the true proportion of people who have recently had the flu is greater than 0.05. A test of hypothesis is conducted.

Part i) What is the null hypothesis?

A. The sample proportion of residents who have recently had the flu is greater than 0.05.
B. The sample proportion of residents who who have recently had the flu is lower than 0.05.
C. The true proportion of residents who have recently had the flu is 0.05.
D. The sample proportion of residents who have recently had the flu is 0.05.
E. The true proportion of residents who have recently had the flu is greater than 0.05.
F. The true proportion of residents who have recently had the flu is lower than 0.05.

Part ii) What is the alternative hypothesis?
Mathematics
1 answer:
RideAnS [48]3 years ago
5 0

Answer:

Null hypothesis would be:

C. The true proportion of residents who have recently had the flu is 0.05.

Alternative hypothesis would be:

E. The true proportion of residents who have recently had the flu is greater than 0.05.

Step-by-step explanation:

Hypothesis testing is made to estimate the true population proportion<em> using the sample info. </em>

The purpose is to provide sufficient evidence to support that the true proportion of people who have recently had the flu is greater than 0.05. Therefore null and alternative hypotheses use this proportion.

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A random sample of 850 births included 434 boys. Use a 0.10 significance level to test the claim that 51.5​% of newborn babies a
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Answer:

A

Null hypothesis: H0: p = 0.515

Alternative hypothesis: Ha ≠ 0.515

z = -0.257

P value = P(Z<-0.257) = 0.797

Decision; we fail to reject the null hypothesis. That is, the results support the belief that 51.5​% of newborn babies are​ boys

Rule

If;

P-value > significance level --- accept Null hypothesis

P-value < significance level --- reject Null hypothesis

Z score > Z(at 90% confidence interval) ---- reject Null hypothesis

Z score < Z(at 90% confidence interval) ------ accept Null hypothesis

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

For the case above;

Null hypothesis: H0: p = 0.515

Alternative hypothesis: Ha ≠ 0.515

Given;

n=850 represent the random sample taken

Test statistic z score can be calculated with the formula below;

z = (p^−po)/√{po(1−po)/n}

Where,

z= Test statistics

n = Sample size = 850

po = Null hypothesized value = 0.515

p^ = Observed proportion = 434/850 = 0.5106

Substituting the values we have

z = (0.5106-0.515)/√(0.515(1-0.515)/850)

z = −0.256677

z = −0.257

To determine the p value (test statistic) at 0.10 significance level, using a two tailed hypothesis.

P value = P(Z<-0.257) = 0.797

Since z at 0.10 significance level is between -1.645 and +1.645 and the z score for the test (z = -0.257) which falls with the region bounded by Z at 0.10 significance level. And also the one-tailed hypothesis P-value is 0.797 which is greater than 0.10. Then we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that at 10% significance level the null hypothesis is valid.

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