When graphing to check for normality and outliers, if you determine that a problem is using two independent

Make sure you do the following:

1. Type your name on your paper

2. Under your name, put STAT 250 with your correct section number (e.g. STAT 250-xxx)

3. Type MINITAB Assignment 5 centered on Page 1.

4. Number and letter the answers accordingly and keep the problems in order.

5. Use complete and coherent sentences to answer the questions.

6. Upload your assignment onto blackboard as a Word document.

7. Remember, you must earn a minimum score of 50 on this assignment to drop your lowest Minitab.

Note: When graphing to check for normality and outliers, if you determine that a problem is using two independent samples, produce separate graphs for each sample. If you determine that a problem is using a matched pairs design, only produce graphs of the column of differences.

1. Pollution index measurements were recorded for eight different areas in a city during rush hour and non-rush hour traffic:

Is there sufficient evidence to show that pollution levels increase during rush hour traffic?

1. What test are you using? Why? What is (are) the parameter(s) we are conducting inference on? Choose one of the following symbols (_D(the mean difference from a matched pairs design)__₂ (the mean difference from independent samples); p, or p₁ – p₂) and describe it in words.

1. Depending on your answer to part (a), construct one or two probability plots and one or two boxplots to visualize the distribution(s) of your sample data. If you construct two probability plots and two boxplots, please construct two separate Minitab probability plots and one Minitab boxplot displaying both boxes on the same graph. Also, properly title and label your graphs. Copy and paste these graphs into your assignment. Below the graphs, answer the following questions.

   1. Are there any major deviations from normality?

   2. Are there any outliers present?

   3. Is it appropriate to conduct statistical inference procedures, why or why not?

If the answer to part iii is no, do not complete the rest of #1.

1. At the 0.05 significance level, test the claim that the pollution levels increase during rush hour traffic.

   1. State the null and alternative hypotheses.

   2. State the significance level for this problem.

   3. Calculate the test statistic

   4. Calculate the P-value and include the probability notation statement.

   5. State whether you reject or do not reject the null hypothesis.

   6. State your conclusion in context of the problem (i.e. interpret your results).

1. For the above situation, construct a 96.2% confidence interval for the above data. Interpret the confidence interval.

1. Researchers collected samples of water from streams in a mountain range to investigate the effects of acid rain. They measured the pH (acidity) of the water (a lower pH means the water is more acidic). They then classified the steams with respect to the kind of substrate (type of rock on which they flow). Here are the results

Substrate Sample size Sample Mean Sample Standard Deviation

Limestone 41 7.7 2.2

Shale 33 6.8 1.7

Is there sufficient evidence that there is a significant difference in the acidity of streams that flow on limestone and on shale?

1. What is (are) the parameter(s) we are conducting inference on? Choose one of the following symbols (_D(the mean difference from a matched pairs design)__₂ (the mean difference from independent samples); p, or p₁ – p₂) and describe it in words.

1. Are the conditions satisfied? Why or why not?

If the answer to part b is no, do not complete the rest of #2.

1. At the 0.05 significance level, can the researcher conclude from these data that there is a significant difference between the mean acidity of the streams that flow on limestone and on shale?

   1. State the null and alternative hypotheses.

1. State the significance level for this problem.

1. Calculate the test statistic.

1. Calculate the P-value and include the probability notation statement.

1. State whether you reject or do not reject the null hypothesis.

1. State your conclusion in context of the problem (i.e. interpret your results).

1. It has been suggested that global warming may increase the frequency of hurricanes. The data show the number of hurricanes recorded annually before and after 1970.

Before (1944 – 1969) 3 3 1 2 4 3 8 5 3 4 2 6 2 2 5 2 2 7 1 2 6 1 3 1 0 5

After (1970-1998) 2 1 0 1 2 3 2 1 2 2 2 3 1 1 1 3 0 1 3 2 1 2 1 1 0 5 6 1

1. What is (are) the parameter(s) we are conducting inference on? Choose one of the following symbols (_D(the mean difference from a matched pairs design)__₂ (the mean difference from independent samples); p, or p₁ – p₂) and describe it in words.

1. Construct a normal probability plot and a boxplot to visualize the distribution of your sample data. Copy and paste these graphs into your assignment. Below the graphs, answer the following questions.

   1. Are there any major deviations from normality?

   2. Are there any outliers present?

   3. Is it appropriate to conduct statistical inference procedures, why or why not?

If the answer to part iii is no, do not complete the rest of #3.

1. At the 0.01 significance level, can you conclude that yearly occurrence of hurricanes have increased after 1970?

   1. State the null and alternative hypotheses.

   2. State the significance level for this problem.

   3. Calculate the test statistic.

   4. Calculate the P-value and include the probability notation statement.

   5. State whether you reject or do not reject the null hypothesis.

   6. State your conclusion in context of the problem (i.e. interpret your results).

1. In the 1980’s it was believed that congenital abnormalities affected about 5% of the nation’s children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 384 children and found that 23 of them showed signs of abnormality.

1. What is (are) the parameter(s) we are conducting inference on? Choose one of the following symbols (_D(the mean difference from a matched pairs design)__₂ (the mean difference from independent samples); p, or p₁ – p₂) and describe it in words.

1. Construct a 95% confidence interval for the above data. Interpret the confidence interval.

1. Construct a 95% confidence interval for the above data using the Plus Four Estimate. Interpret the confidence interval.

1. Is there sufficient statistical evidence at level of significance to show that the incidence of abnormalities has increased?

1. State the null and alternative hypotheses.

2. State the significance level for this problem.

3. Check the conditions that allow you to use the test statistic, and, if appropriate, calculate the test statistic.

4. Calculate the P-value and include the probability notation statement.

5. State whether you reject or do not reject the null hypothesis.

6. State your conclusion in context of the problem (i.e. interpret your results).

1. 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 consumed the recommended daily allowance of calcium.

1. What is (are) the parameter(s) we are conducting inference on? Choose one of the following symbols (_D(the mean difference from a matched pairs design)__₂ (the mean difference from independent samples); p, or p₁ – p₂) and describe it in words.

1. Construct a 96% confidence interval for the above data. Interpret the confidence interval.

1. Construct a 96% confidence interval for the above data using the Plus Four Estimate. Interpret the confidence interval.

1. At the 0.05 significance level, 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?

   1. State the null and alternative hypotheses.

   2. State the significance level for this problem.

   3. Check the conditions that allow you to use the test statistic, and, if appropriate, calculate the test statistic.

   4. Calculate the P-value and include the probability notation statement.

   5. State whether you reject or do not reject the null hypothesis.

   6. State your conclusion in context of the problem (i.e. interpret your results).

1. If the true population proportion was 0.588, did you commit an error? If so, which type of error did you commit and why? If not, why not? Answer in complete sentences.