A new kind of typhoid shot is being developed by a medical research team. The ol

Question

A new kind of typhoid shot is being developed by a medical research team. The old thphiod shot was known to protect the population for a mean time for 36 months, with a standard deviation of 3 months. To test the time variability of the new shot, a random sample of 23 people were given the new shot. Regular blood tests showed that the sample deviation of protections times was 1.9 months. Using a 0.05 level of significance, test the claim that the new typhoid shot has a smaller variance of protection times.

Explanation / Answer

Solution:

Here, we have to use the Chi square test for population variance.

The null and alternative hypothesis for this test is given as below:

H0: ^2 = 9 versus Ha: ^2 < 9

We are given

Population standard deviation = = 3

Population variance = ^2 = 3^2 = 9

Level of significance = = 0.05

Sample size = n = 23

Sample standard deviation = S = 1.9

Degrees of freedom = n - 1 = 23 – 1 = 22

Lower critical value = 12.3380

The Chi square test statistic formula is given as below:

Chi square = (n – 1)*S^2 / ^2

Chi square = (23 - 1)*1.9^2/3^2

Chi square = 8.824444

P-value = 0.0058

= 0.05

P-value <

So, we reject the null hypothesis

This means there is sufficient evidence to conclude that the new typhoid shot has a smaller variance of protection times.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.