An article in AARP Bulletin (Jan-Feb 2010) | Complete Solution

1.An article in AARP Bulletin (Jan-Feb 2010) reported that women with a high school diploma had average weekly earnings of $520.  Use the Weekly Pay data to test the hypothesis that the overall weekly average earning for women is equal to $520.   What is the test statistic?  Answer to three decimal places.

2.An article in AARP Bulletin (Jan-Feb 2010) reported that women with a high school diploma had average weekly earnings of $520.  Test the hypothesis that the overall weekly average earning for women is equal to $520 using the Weekly Pay data.   What is the critical value for this test when the level of significance is .05?  Answer to three decimal places.  Note that we do not know the true standard deviation in the population so we are using the value in the sample as and estimate.  Because we do not know the true standard deviation the hypothesis test will be a t test.

3.Using information from the previous questions on the weekly pay for women do you reject or fail to reject the null hypothesis that the average pay for all women is $520 per week?

fail to reject because the test statistic is greater than the critical value.

fail to reject because the test statistic is less than the critical value.

reject because the test statistic is greater than the critical value.

reject because the test statistic is less than the critical value.

4.The Department of Health and Human Services gives thepoverty guideline in 2014 for a family of six as $31,970.  That translates to a weekly amount of about $615.  Use the Weekly Pay data to test the hypothesis that the average earnings for a woman are not enough to meet the poverty guidelines for a family of six and ignore the fact that the data and guidelines are for two separate years.    Note the null hypothesis in this example is that average pay>=615.  What is the test statistic?  Answer to three decimal places.

5.The Department of Health and Human Services gives the poverty guideline in 2014 for a family of six as $31,970.  That translates to a weekly amount of about $615.  Use the Weekly Pay data to test the hypothesis that the average earnings for a woman are not enough to meet the poverty guidelines for a family of six and ignore the fact that the data and guidelines are for two separate years.    Note the null hypothesis in this example is that average pay>=615.  What is the critical value for alpha=.05?  You might want to draw this out showing the rejection region to verify that your answer makes sense.  Answer to three decimal places.

6. Suppose that a restaurant launched a new advertising campaign in conjunction with a new menu.  After one month they take a random sample of 250 bills (tables) and find an average bill of 73.4.  In that sample they also find the standard deviation is 38.6.  Conduct a hypothesis test to determine whether the new campaign and menu have increased the average bill above the previous average of 71.6.  Hint, the null hypothesis is that mu<=71.6 and we assume that the standard deviation is unkonwn so we use the estimate of 38.6 from the sample.  What is the test statistic? Answer to three decimal places.

7.Customers service representatives attempt to sell new products to certain customers when they call in.  In order for the "cross sell" to be profitable service representatives need to get more than 10% of customers to buy the new product.  In a sample of one team of service representatives they offered the new product to 500 customers and 67 made the purchase.  Management wants proof at the .01 level of significance that the team sells to more than 10% of customers.  Note that the null hypothesis is that the population proportion<=.1.  What is the test statistic?  Answer to three decimal places.

8.Based on the test statistic you found above for the 500 customers with 67 buying the product and the alpha value of .01 what conclusion do you draw?

Reject the null hypothesis;  there is strong evidence that the team sells to greater than 10% of the target customers.

Fail to reject the null hypothesis; there is not strong evidence that the team sells to greater than 10% of the target customers.

Reject the null hypothesis;  there is not strong evidence that the team sells to greater than 10% of the target customers.

Fail to reject the null hypothesis; there is strong evidence that the team sells to greater than 10% of the target customers.

9.The p-value is

1 minus the power of a test.

the exact or observed level of significance.

the probability of a Type II error.

the same as the critical value.

10.For a given standard error, the larger the difference between two point estimates the greater the p-value for a test of the equality of means.  (Hint, try it with two sets of numbers and the same standard error and see which one has the larger p-value then look at it to see if that was a coincidence or if that will always be the case).

     True False
    The test statistic for a hypothesis test concerning the value of a population mean when the standard deviation is known and the sample has more than 30 observations follows which distribution?

    t

    z

    F

    Chi square

1 points   

    The test statistic for a hypothesis test concerning the value of a population mean when the population standard deviation is not known and the sample has more than 30 observations follows which distribution?

    t

    z

    F

    Chi square

1 points   

    The test statistic for a hypothesis test concerning a population proportion follows which distribution?

    t

    z

    F

    Chi square

1 points   

  A Type I error is when we fail to reject the null hypothesis even though it is false. True False