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Last year there was a pandemic caused by xyz virus in the city of Abc. The population of the city is 15 million. The health authorities of the city are estimating that more than 3% of the people of this city were infected by this virus. In order to test this statement, they collected a sample of 1000 individuals of this city and conducted an antibody test on them. The results of the analysis showed that 40 individuals out of those 1000 people got infected during the pandemic. Is there evidence to support that more than 3% of the population of the city got infected by the virus? Use hypothesis testing.

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Answer:

There is significant evidence to support that more than 3% of the population of the city got infected by the virus.

Step-by-step explanation:

x = 40 ; n = 1000

phat = x / n = 40 / 1000 = 0.04 = 4%

H0 : p = 0.3

H1 : p > 0.3

The test statistic :

(Phat - P) ÷ √(p(1 - p) / n)

1 - p = 1 - 0.3 = 0.7

(0.4 - 0.3) ÷ √(0.3(0.7) / 1000)

0.1 ÷ 0.0144913

= 6.9

Pvalue ; Using the Pvalue from Zstatistic calculator :

Pvalue < 0.00001

Reject H0, if Pvalue < α

0.00001 < α ; We reject H0 ; Hence, there is significant evidence to support that more than 3% of the population of the city got infected by the virus.

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