1.A professor measured the time (in seconds) required to catch a falling meter stick for 19 randomly selected students' dominant and non-dominant hand. The professor claims that the reaction time in an individual's dominant hand is less than the reaction time in their non-dominant hand. At the 0.10 significance level, test the claim that the reaction time in an individual's dominant hand is less than the reaction time in their non-dominant hand. (The results can be found in the first two columns of the Minitab file).
a.What is (are) the parameter(s) we are conducting inference on? (You may state your answer in words or symbols).

b.Depending on your answer to part (a), construct one or two histograms and one or two boxplots to visualize the distribution(s) of your sample data. If you construct two histograms and two boxplots, please construct two separate Minitab histograms and one Minitab boxplot displaying both boxes on the same graph. Also, properly title and label your graphs and use cut points and 5 classes for your histogram(s). Copy and paste these graphs into your assignment. Below the graphs, answer the following questions.
i.Are there any major deviations from normality?
ii.Are there any outliers present?
iii.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.

c.At the 0.10 significance level, test the claim that the reaction time in an individual's dominant hand is less than the reaction time in their non-dominant hand.
i.State the null and alternative hypotheses.
ii.State the significance level for this problem.
iii.Calculate the test statistic.
iv.Calculate the P-value and include the probability notation statement.
v.State whether you reject or do not reject the null hypothesis.
vi.State your conclusion in context of the problem (i.e. interpret your results).
d.For the above situation, construct a 96.2% confidence interval for the above data. Interpret the confidence interval as we learned in class.

Note: For part d, to earn full credit, show how you obtained the critical value for the confidence interval in Minitab, write out the formula you would use, and the steps necessary to construct the confidence interval.

2.A researcher wanted to know whether there was a difference in the level of understanding among students learning Minitab based on the style of instruction. In a previous semester of STAT 250, Section 1 was taught Minitab with video tutorials and Section 2 was taught Minitab with written instructions. One simple random sample of 28 was taken from each section and the students in each sample were given a Minitab quiz that tested basic procedures. The data provided in Minitab represents the quiz scores the students received. At the 0.01 significance level, can the researcher conclude from these data that there is a significant difference in quiz scores between the two methods of instruction?

a.What is (are) the parameter(s) of interest?

b.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 one graph. Remember to properly title and label these graphs. Copy and paste these graphs into your assignment. Below the graphs, answer the following questions.
i.Are there any major deviations from normality?
ii.Are there any outliers present?
iii.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 #2.

c.At the 0.01 significance level, can the researcher conclude from these data that there is a significant difference in quiz scores between the two methods of instruction?
i.State the null and alternative hypotheses.
ii.State the significance level for this problem.
iii.Calculate the test statistic.
iv.Calculate the P-value and include the probability notation statement.
v.State whether you reject or do not reject the null hypothesis.
vi.State your conclusion in context of the problem (i.e. interpret your results).

d.Construct a 95% confidence interval for the above data. Interpret this confidence interval.
Note: To earn full credit, explain how you obtained the critical value for the confidence interval, write out the formula you would use and the steps necessary to construct the confidence interval.


3.In an attempt to increase business on Monday nights, a restaurant offers a free dessert with every dinner order. Before the offer, the mean number of dinner customers on Monday was 150. The numbers of diners on a random sample of 12 days while the offer was in effect are selected. Can you conclude that the mean number of diners increased while the free dessert offer was in effect?

a.What is (are) the parameter(s) of interest?

b.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.
i.Are there any major deviations from normality?
ii.Are there any outliers present?
iii.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.

c.At the 0.05 significance level, can you conclude that the mean number of diners increased from 150 while the free dessert offer was in effect?
i.State the null and alternative hypotheses.
ii.State the significance level for this problem.
iii.Calculate the test statistic.
iv.Calculate the P-value and include the probability notation statement.
v.State whether you reject or do not reject the null hypothesis.
vi.State your conclusion in context of the problem (i.e. interpret your results).

d.Construct a 99% confidence interval for the above data. Interpret the confidence interval.


4. According to a report of the Nielsen Company, 65% of Internet searches used Google as the search engine. Assume that a sample of 13 searches is studied. Let the random variable be the number of searches where Google was used.

(a)What is the name of the probability distribution of X? Write out the setting (i.e. write out the four requirements of a particular setting that you learned in class).
(b)Produce a table that lists the possible values of the random variable and the corresponding probabilities of each value's occurrence.
(c)What is the mean of this distribution? Show work using the formula.
(d)What is the standard deviation of this distribution? Show work using the formula.
(e)Calculate the probability that of the 13 searches analyzed, at least 8 of those searches used Google. Display a Minitab Graph with the correct portion shaded as the answer to this question. Then, verify your answer with using the table you displayed in part (b).


5.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 finds that 36 of them consume the recommended daily allowance of calcium.

a.If we conduct statistical inference above, what is (are) the parameter(s) of interest?

b.Construct a 96% confidence interval for the above data. Interpret the confidence interval as we learned in class. Show your work using the formulas.

c.Construct a 96% confidence interval for the above data using the Plus Four Estimate. Interpret the confidence interval as we learned in class. Show your work using the formulas.
d.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?
i.State the null and alternative hypotheses.
ii.State the significance level for this problem.
iii.Check the conditions that allow you to use the test statistic, and, if appropriate, calculate the test statistic.
iv.Calculate the P-value and include the probability notation statement.
v.State whether you reject or do not reject the null hypothesis.
vi.State your conclusion in context of the problem (i.e. interpret your results)