STAT 250-004 Data Analysis Assignment 4 | Complete Solution

STAT 250-004 Data Analysis Assignment 4

Problem 1: Got Milk

According to the U.S. Department of Agriculture, 58.8% of males between 20 and 39 years old consume the minimum daily requirement of calcium.  After an aggressive “Got milk” advertising campaign, the USDA conducted a survey of 55 randomly selected males between the ages of 20 and 39 and found that 36 of them consume the recommended daily allowance of calcium.

    Construct a 90% confidence interval for the above data.  Show your work using the formulas and verify your work using StatCrunch.

    At the  = 0.01, is there evidence to conclude that the percentage of males between the ages of 20 and 39 who consume the recommended daily allowance of calcium has increased?  Conduct a full hypothesis test by following the steps below.

    State the null and alternative hypotheses.
    State the significance level for this problem.
    Check the conditions that allow you to use the test statistic, and, if appropriate, calculate the test statistic.
    Calculate the p-value and include the probability notation statement.
    State whether you reject or do not reject the null hypothesis.
    State your conclusion in context of the problem (i.e. interpret your results).

    Explain the connection between the confidence interval and the hypothesis test in this problem (discuss in relation to the decision made from your hypothesis test).

Problem 2: Mercury in Freshwater Fish

Experts believe that 20% of all freshwater fish in the United States have such a high level of mercury that they are dangerous to eat.  Suppose a fish market has 250 fish tested and 60 of them have dangerous levels of mercury.  Test the hypothesis that this sample is not from a population with 20% dangerous fish.  Use  = 0.10.

    State the null and alternative hypotheses.
    State the significance level for this problem.
    Check the conditions that allow you to use the test statistic, and, if appropriate, calculate the test statistic.
    Calculate the p-value and include the probability notation statement.
    State whether you reject or do not reject the null hypothesis.
    State your conclusion in context of the problem (i.e. interpret your results).
    Use StatCrunch to verify your test statistic and p-value.

Problem 3: Explore the Confidence Interval Applet

Start in StatCrunch by clicking Applets  Confidence Intervals  for a proportion.  Choose any values for p (between 0.01 and 0.99), set the confidence level between 90% and 99%, and choose a sample size where np ̂ > 10; n(1 - p ̂) > 10.  Click Compute!  Then, once your first 100 intervals have been constructed, click the 1000 intervals button.  You will now have 1100 total intervals.  Copy and paste your graph of many confidence intervals (your graph will represent intervals 1001 to 1100).  Discuss the percentage capturing p in relation to the correct confidence interval interpretation learned in class.

Please complete the entire applet again using the same p and confidence level you chose, but this time, choose a small enough sample size where np ̂ < 10; n(1 - p ̂) < 10.  Repeat the process above to obtain 1100 intervals.  Again, copy and paste your graph and discuss the percentage capturing p in relation to the correct confidence interval interpretation learned in class.

Problem 4: Smoking Bans

On November 3 – 5, 2010, the Gallup Organization surveyed 1028 adult Americans and found that 463 said they supported a ban on smoking in public places.  More recently, on October 15 – 17, 2014, the Gallup Organization surveyed 997 adult Americans and found that 550 supported a ban on smoking in public places.    

    Construct a 93% confidence interval for the above data.  Show your work using the formulas and verify your work using StatCrunch.

Continued below
    Construct a 98% confidence interval for the above data.  Show your work using the formulas and verify your work using StatCrunch.

    Interpret the confidence interval calculated in part (b) as we learned in class.  

    At the  = 0.05, is there evidence to conclude that a difference in opinion exists over time?  Conduct a full hypothesis test by following the steps below.

    State the null and alternative hypotheses.
    State the significance level for this problem.
    Check the conditions that allow you to use the test statistic, and, if appropriate, calculate the test statistic.
    Calculate the p-value and include the probability notation statement.
    State whether you reject or do not reject the null hypothesis.
    State your conclusion in context of the problem (i.e. interpret your results).
    Use StatCrunch to verify your test statistic and p-value.

Note: To add formulas to a Word document, go above to Insert  object  Microsoft Equation 3.0.  You can also copy and paste the following formulas when you need them (double click on the formula to replace the letters with numbers).