A new kind of typhoid shot is being developed by a medical research team. The ol
ID: 3153893 • Letter: A
Question
A new kind of typhoid shot is being developed by a medical research team. The old typhoid shot was known to protect the population for a mean time of 36 months, with a standard deviation of 3 months. To test the time variability of the new shot, a random sample of 24 people were given the new shot. Regular blood tests showed that the sample standard deviation of protection times was 1.9 months. Using a 0.10 level of significance, test the claim that the new typhoid shot has a smaller variance of protection times. Find a 99% confidence interval for the population standard deviation.
Explanation / Answer
a)
As given,
alpha = 0.10 [ANSWER]
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Formulating the null and alternative hypotheses,
Ho: sigma^2 = 9
Ha: sigma^2 < 9
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b)
As we can see, this is a left tailed test.
Getting the test statistic, as
s = sample standard deviation = 1.9
sigmao = hypothesized standard deviation = 3
n = sample size = 24
Thus, chi^2 = (N - 1)(s/sigmao)^2 = 9.225555556 [ANSWER]
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df = N - 1 = 23 [DEGREES OF FREEDOM]
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OPTION A: A normal distribution [ANSWER]
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c)
As this is a left tailed test,
Pvalue = 0.004862273 [ANSWER]
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d)
As P < 0.10, we reject Ho:
OPTION D: reject Ho; data is significant. [ANSWER]
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e)
OPTION B: Reject Ho, there is sufficient evidence... [ANSWER]
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