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    Question 1

    A hypothesis test is to be performed for a population proportion. For the given sample data and null hypothesis, compute the value of the test statistic, z = p-p0/(squareroot)p0(1-p0)/n

    Out of 69 observations, 67% were successes. H0: p = 0.54.

    1.291
    2.167
    0.008
    1.723

    Question 2

    Use the one-proportion z-test to perform the specified hypothesis test. Use the critical-value approach.

    x = 610, n = 1500, H0: p≤ 0.40, Ha: p > 0.40, α = 0.01

    z = 0.53; critical value = 2.33; do not reject H0

    z = 0.62; critical value = 2.575; reject H0

    z = 0.62; critical value = 2.33; do not reject H0

    z = 0.53; critical value = 2.575; do not reject H0

    Question 3

    Provide an appropriate response.

    Find the standardized test statistic t for a sample with n = 15, = 7.2, s = 0.8, and if Round your answer to three decimal places.

    1.631

    1.452

    1.728

    1.312
    Question 4

    Test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed.

    Claim μ = 24; α = 0.01. Sample statistics: = 25.2, s = 2.2, n = 12

    t0 = ±3.106, standardized test statistic ≈ 1.890, fail to reject H0; There is not sufficient evidence to reject the claim.

    t0 = ±3.106, standardized test statistic ≈ 1.890, reject H0; There is sufficient evidence to reject the claim.

    t0 = 3.106, standardized test statistic ≈ 1.890, fail to reject H0; There is not sufficient evidence to reject the claim.

    Question 5

    Find the critical value X 2/0 and rejection region for the type of chi-square test with sample size n and level of significance α.

    Right-tailed test,
    n = 18, α = 0.01

    χ20 = 35.718; χ2 > 35.718
    χ20 = 27.587; χ2 > 27.587
    χ20 = 30.181; χ2 > 30.181
    χ20 = 33.409; χ2 > 33.409

    Question 6

    Find the critical values for t0 a sample with n = 12 and α = 0.01 if H0: μ = 20.

    ±2.201
    ±3.106
    ±1.796
    ±2.718

    Question 7

    Compute the standardized test statistic, X2, to test the claim σ2 ≥ 12.6 if n = 15, s2 = 10.5, and

    12.823
    11.667
    23.891
    8.713

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    https://brainmass.com/statistics/type-i-and-type-ii-errors/critical-value-test-statistic-some-test-questions-613766

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    Solution Preview

    Question 1

    A hypothesis test is to be performed for a population proportion. For the given sample data and null hypothesis, compute the value of the test statistic, z = p-p0/(squareroot)p0(1-p0)/n

    Out of 69 observations, 67% were successes. H0: p = 0.54.

    1.291
    2.167
    0.008
    1.723
    Test statistic=(0.67-0.54)/[sqrt(0.54*0.46/69)]=2.167

    Question 2

    Use the one-proportion z-test to perform the specified hypothesis test. Use the critical-value approach.

    x = 610, n = 1500, H0: p≤ 0.40, Ha: p > 0.40, α = 0.01

    z = 0.53; critical value = 2.33; do not reject H0

    z = 0.62; critical value = 2.575; reject H0

    ...

    Solution Summary

    The solution gives detailed steps on finding critical value and test statistic for some t test questions.

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