March 29, 2017

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A recent article in a computer magazine suggested that the mean time to fully learn a new software program is 40 hours. A sample of 100 first time users of a new statistics program revealed the mean time to learn it was 39 hours with the standard deviation of 5 hours. At the 0.05 significance level, can we conclude that users learn the package in less than a mean of 40 hours?

a. State the null and alternate hypotheses.
b. State the decision rule.
c. Compute the value of the test statistic.
d. Compute the p-value.
e. What is your decision regarding the null hypothesis? Interpret the result.

  • college Math - ,

    Ho: µ = 40 --->meaning the population mean is equal to 40.

    H1: µ < 40 ---> meaning the population mean is less than 40.

    This will be a one-tailed test because the alternative hypothesis is showing a specific direction.

    Use a z-test. Find the significance level for a one-tailed test using a z-table. Compare the test statistic from the z-test to the value from the z-table. If the test statistic exceeds the value in the table, then reject the null and conclude µ < 40. The p-value is the actual level of the test statistic found using a z-table.

    Here is a z-test formula to get you started:

    z = (sample mean - population mean)/(standard deviation divided by the square root of the sample size)

    Sample mean = 39
    Population mean = 40
    Standard deviation = 5
    Sample size = 100

    Fill the values into the formula and compute the test statistic.

    I'll let you take it from here.

    I hope this will help get you started.

  • college Math - ,

    P-value of 0.894<0.05

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