A new kind of typhoid shot is being developed by a medicalresearch team. The old typhoid shot was known to protect thepopulation for a mean time of 36 months, with a standard deviationof 3 months. To test the time variability of the new shot, a randomsample of 21 people were given the new shot. Regular blood testsshowed that the sample standard deviation of protection times was1.3 months. Using a 0.05 level of significance, test the claim thatthe new typhoid shot has a smaller variance of protectiontimes.

(a) What is the level of significance?


State the null and alternate hypotheses.

H_o: σ² = 9;H₁: σ² >9H_o: σ² = 9;H₁: σ² <9    H_o:σ² < 9; H₁:σ² = 9H_o: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 originaldistribution?

We assume a uniform population distribution.We assume aexponential population distribution.    Weassume a binomial population distribution.We assume a normalpopulation distribution.

(c) Find or estimate the P-value of the sample teststatistic.

P-value > 0.1000.050 < P-value <0.100    0.025 < P-value <0.0500.010 < P-value < 0.0250.005 <P-value < 0.010P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject orfail to reject the null hypothesis?

Since the P-value > α, we fail to rejectthe null hypothesis.Since the P-value > α, wereject the null hypothesis.    Since theP-value ≤ α, we reject the null hypothesis.Sincethe P-value ≤ α, we fail to reject the nullhypothesis.

(e) Interpret your conclusion in the context of theapplication.

At the 5% level of significance, there is insufficient evidenceto conclude that the new typhoid shot has a smaller variance ofprotection times.At the 5% level of significance, there issufficient evidence to conclude that the new typhoid shot has asmaller variance of protection times.    

(f) Find a 90% confidence interval for the population standarddeviation. (Round your answers to two decimal places.)

lower limit
upper limit   Â

Interpret the results in the context of the application.

We are 90% confident that σ lies within thisinterval.We are 90% confident that σ lies below thisinterval.    We are 90% confident thatσ lies above this interval.We are 90% confident thatσ lies outside this interval.