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    Critical Value, Sample Statistic & Probability Value

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    1. Suppose that the shoe company Alta Claims that their mean weekly sales are $17,350. A random sample of 35 weeks yields a sample mean of $10,450. With a sample standard deviation of s =$1500.
    Given that the pair of hypothesis that correspond to the claim are
    H0: µ = 17,350
    H1: µ ≠ 17,350

    Find the critical value for the hypothesis test. Assume that the significance level is α = 0.08.
    Critical values = +/-
    Round your final answer to two decimal places.

    2. Suppose that an insurance agent for State Ranch claims that the average life insurance policy premium that he sells is $450 per year. A sample of 40 customers yields a mean of x =$475 and a standard deviation of s = $85. You decide to test his claim at the α = 0.05 significance level.
    If the hypothesis are
    H0: µ = 450
    H1: µ ≠ 450

    With critical values of ±1.96, compute the sample statistic, and choose the appropriate conclusion.
    Z =
    Round your answer o two decimal places.

    3. Suppose that the company CEO for Quitters, Inc. claims that the average severance package for an employee at his company is $450,000. You decide to test his claim using a significance level of α = 0.04. A sample of 40 employees yields a mean of x = $414,845 with a sample standard deviation of s = $125,575. First, you set up your hypothesis as follows

    H0: µ = $450,000 (claim)
    H1: µ = $450,000

    Then you compute your sample statistic, get the following

    Z = 414.845 - 450,000
    125,575
    √40
    = -1.77

    Compute the probability of getting a sample statistic at least as extreme as z = -1.77, and interpret this probability value.

    Probability =
    Final answer to two decimal places.

    4. Suppose a private university claims that more than 2/3 of their students graduate within for years. A random survey of 300 alumni finds that 190 of them graduated within 4 years.

    Given that the pair of hypothesis that corresponds to the claim are
    H0: p ≤ 0.67
    H1: p > 0.67

    Find the critical value for the hypothesis test. Assume the significance level is α = 0.01.

    Remember that this is a right-tailed test, so your critical value will be positive. Remember also that in one-tailed test, you don't have to cut your α-value in half.
    Critical value =
    Round your final answer to two decimal places.

    5. Suppose that an insurance agent for Almost Heaven insurance claims that less than 20% of his life insurance policies ever have to 'pay out'. You decide to test his claim at the α = 0.02 significance level. A sample of 75 policies from the last year finds that 30 of them had to pay out.
    If the hypothesis are

    H0: p ≥0.20
    H1: p < 0.20

    With a critical value of -2.05, compute the sample statistic, and choose the appropriate conclusion.

    Z =
    Round the sample statistic to two decimal places.

    6. Suppose that the CEO of U-Store-it claims that more than 2/3 of his employees carry secondary health insurance. You decide to test his claim using a significance level of α = 0.05. A sample of 150 employees finds that 108 of them carry secondary health insurance.
    First, you set up your hypothesis as follows:

    H0: p ≤ 0.67
    H1: p > 0.67(claim)

    Then you compute your sample statistic, and get the following:

    Z = 108 - 0.67
    150________
    √0.67 x 0.33
    150
    =1.30

    Compute the probability of getting a sample statistic as least as extreme as z = 1.30, and interpret this probability value. Remember that in one -tailed test such as this, you do not need to multiply your p-value by two.

    Probability =
    Round your final answer to two decimal places.

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    https://brainmass.com/statistics/hypothesis-testing/critical-value-sample-statistic-probability-value-392902

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    This solution provides assistance determining the critical value, the sample statistic and the probability value.

    $2.19

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