The Ebola virus seems to have surged recently with a new outbreak in West Africa

Question

The Ebola virus seems to have surged recently with a new outbreak in West Africa and the first confirmed case in the US. The World Health Organization (WHO) reported on September 5, 2014 the number of confirmed cases in African over the prior 21 days was 37.52 per day. It has been stated that Guinea has a much lower average than the other affected countries, with a lower average per day. Data was collected from Guinea over the same 21 days and found they had an average of 28.58 confirmed cases per day with a standard deviation of 9.48.

At the 0.01 level, can you say that Guinea really does have a lower average than the rest of Africa?

1. The hypothesis
2. The critical value
3. The test statistic
4. The decision you made, why you made it, and how does it answer the original question.

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: > 37.2

Alternative hypothesis: < 37.2

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 2.069

DF = n - 1 = 21 - 1

D.F = 20

t = (x - ) / SE

t = - 4.32

tcritical = 2.528

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of - 4.32. We use the t Distribution Calculator to find P(t < - 4.32) = 0.000166

Interpret results. Since the P-value (0.000166) is less than the significance level (0.01), we have to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that Guinea has a much lower average than the other affected countries.

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