Reference no: EM132168193
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 27 people were given the new shot. Regular blood tests showed that the sample standard deviation of protection times was 2.1 months. Using a 0.05 level of significance, test the claim that the new typhoid shot has a smaller variance of protection times. (a) What is the level of significance?
State the null and alternate hypotheses.
Ho: σ2 < 9; H1: σ2 = 9
Ho: σ2 = 9; H1: σ2 > 9
Ho: σ2 = 9; H1: σ2 ≠ 9
Ho: σ2 = 9; H1: σ2 < 9
(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)
What are the degrees of freedom?
What assumptions are you making about the original distribution?
We assume a normal population distribution.
We assume a binomial population distribution.
We assume a exponential population distribution.
We assume a uniform population distribution.
(c) Find or estimate the P-value of the sample test statistic.
P-value > 0.100
0.050 < P-value < 0.100
0.025 < P-value < 0.050
0.010 < P-value < 0.025
0.005 < P-value < 0.010
P-value < 0.005
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?
Since the P-value > α, we fail to reject the null hypothesis.
Since the P-value > α, we reject the null hypothesis.
Since the P-value ≤ α, we reject the null hypothesis.
Since the P-value ≤ α, we fail to reject the null hypothesis.
(e) Interpret your conclusion in the context of the application.
At the 5% level of significance, there is insufficient evidence to conclude that the new typhoid shot has a smaller variance of protection times.
At the 5% level of significance, there is sufficient evidence to conclude that the new typhoid shot has a smaller variance of protection times.
(f) Find a 90% confidence interval for the population standard deviation. (Round your answers to two decimal places.)
lower limit
upper limit
Interpret the results in the context of the application.
We are 90% confident that σ lies above this interval.
We are 90% confident that σ lies outside this interval.
We are 90% confident that σ lies below this interval.
We are 90% confident that σ lies within this interval.