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- From: Mathematics, Statistics and Probability
- Posted on: Mon 18 Jan, 2016
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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 0.05 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 Excel file).
a. If we conduct statistical inference for this problem, 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 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. 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 0.05 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. Construct a 97.5% 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 101, 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 the Excel file 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. If we conduct statistical inference above, what is (are) the parameter(s) of interest?
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 one graph. 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. How much time do undergraduate students spend each day reading and sending email? A survey was conducted by a graduate student asking students in the library the above question. The responses (in minutes per day) of the first 50 students were recorded in Minitab. At the 0.10 significance level, can the students infer from these data that the mean amount of time spent by all students reading and sending email daily differs from 90 minutes? Data is provided in Excel file.
a. If we conduct statistical inference above, what is (are) the parameter(s) of interest?
b. Construct a 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 0.10 significance level, can the student infer from these data that the mean amount of time spent by all students reading and sending email daily differs from 90 minutes?
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).
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