Computing critical values by null and alternative hypotheses

Reference no: EM1313636

Q1) Consider X1, X2, ..., Xn be random sample from normal population N(H,σ2) with unidentified mean and variance. With parameters represented as θ = (θ1, θ2) = (H,σ2), use a likelihood ratio method to create a hypothesis test for 2 2 H0 :σ =σ 0 . First get likelihood ratio Λ and then illustrate that instead of Λ, test statistic Λ' (n-1)S(squared) / σ squared)) must be used, where S2 is sample variance. Therefore, establish that likelihood ratio test for variance of single normal population is the same to result got for null hypothesis significance testing of a single variance.

Q2) Create a set of 100 observations from population whose distribution is N(503,7.5). c. Create a hypothesis test to check if standard deviation is equal to 7.5 in two ways:

i) By constructing null and alternative hypotheses, computing critical values, and comparing test statistic to critical value.

ii) By calculating P-value of test statistic.

iii) Evaluate the results.

Reference no: EM1313636

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