Table 2. Results of two coins tossed simultaneously 40 times.Outcomes(OIE)Observed Expected(0)(E)2 heads1 head, 1 tail2 tailsTotals1. State a null hypothesis for this experiment.2. How many degrees of freedom are there?3. What is the critical value of the X² for a = 0.05?4. Do you accept or reject the null hypothesis? Why?Activity 3Table 3. Results of three coins tossed simultaneously 64 times.OutcomesObserved Expected(0)(E)(O - E)3 heads2 heads; 1 tail1 heads; 2 tails3 tailsTotalsXXXXXX1. State a null hypothesis for this experiment.2. How many degrees of freedom are there?3. What is the critical value of the X² for a = 0.05?XXXXXX4. Do you accept or reject the null hypothesis? Why?(OE)²(OE)²/EXXXXX X² =(O.DE)²(OE)²/EXXXXXX X²= NameWorksheet- Probabilities and StatisticsMore Review:1. In statistics what is a null hypothesis?2. When the deviations are large between the observed and the expected values, what is theresult for the calculated chi-square value?3. How do you calculate the number of degrees of freedom for a chi-square test?4. What is the typical probability cut off, at which we reject the null hypothesis?5. What does this P value mean?6. What is the critical X² value for 1 degree of freedom?Activity 1Table 1. Results of one coin tossed 20 times.OutcomesObserved Expected(0)(E)Heads (H)Tails (T)Totals(OE)XXXXXX(OE)² (OE)²/E2. Why would you expect some deviations from the expected?XXXXXX X² =1. Do the observed results correspond exactly to the expected, or is there some variation?3. If Activity 1 had been an experiment, what would the null hypothesis have been?4. Do you accept or reject your null hypothesis for the data in Table 1?Activity 2

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Taxes: The Internal Revenue Service reports that the mean federal income tax paid in the year 2010 was $8040 . Assume that the standard deviation is $4900 . The IRS plans to draw a sample of 1000 tax returns to study the effect of a new tax law. Part 1 of 5 (a) What is the probability that the sample mean tax is less than $7800 ? Round the answer to at least four decimal places. The probability that the sample mean tax is less than $7800 is . Part 2 of 5 (b) What is the probability that the sample mean tax is between $7500 and $8000 ? Round the answer to at least four decimal places. The probability that the sample mean tax is between $7500 and $8000 is . Part 3 of 5 (c) Find the 30th percentile of the sample mean. Round the answer to at least two decimal places. The 30th percentile of the sample mean is $ .…
An elementary school teacher is interesting in knowing if there is a significant difference in the average reading speed of fifth grade boys and girls. She randomly selects 40 fifth grade boys and 40 fifth grade girls for the study. She gives each student several pages of the same book to read. The time it takes them to complete the reading is recorded in minutes. The teacher is trying to determine if there is pervasive evidence to conclude at a = 0.05 there is a difference in average reading speed of fifth grade boys and fifth grade girls. The results are summarized in the following table: 40 10 Boys Girls 40 11 1. What is the population of interest? 2. What claim is being made? 3. Specify the null and alternative hypothesis. Ho: Ha: 4. Should the hypothesis be a one of two tailed test? 5. Is the sample size large enough? How can you tell? 6. What is the level of significance? 7. Graphically construct the rejection region. continued on back...
Using the standard normal table. Look up a z-score of -0.14. What probability do you see there?
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(5) You take a random sample from some population and form a 98% confidence interval for the population mean, a. Which quantity is guaranteed to be in the interval you form? A. 0 B. u C. D. 0.98
“Type I Error Blues,” by David Stein The managers huddled to see if they had won or lost. Did the new process from 2 months before yield data showing a reduction in cost? Or was it merely a matter of chance… Too soon to do the data dance? So they set about the business of crafting a hypothesis test In order to conclude which process was best. With the null hypothesis meaning “status quo”, no change evident They quickly concluded H0 could not stand, as was their true intent. Just one month later, they realized their grave mistake! A Type II error would have been so much safer, for goodness sake. Alas, their final huddle was a sad one with HR Director Bob. He told them to go back to training school as each was now in need of a new job. What was the likely managerial mood and outcome on the days immediately following the (erroneous) conclusion to reject this null hypothesis? What would have been the likely managerial mood and outcome on the days immediately following an…
Evaluate the significance of the p-value. You can think of the p-value as the probability that the null hypothesis is true. A value greater than 0.05 indicates that in more than 1 in 20 (or more than 5%) repetitions of an experiment of the same size, the observed deviation from predicted valuescould have been obtained by chance, even if the null hypothesis is actually true; the data are therefore not significant for rejecting the null hypothesis. Statisticians have arbitrarily selected the 0.05 p-value as the boundarybetween rejecting or not rejecting the null hypothesis. A p-value of less than 0.05 means that you can consider the deviation to be significant, and you can reject the null hypothesis.
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10 It is known that 15% of a large constituency voted for the Working Together Party (WTP) at the last election. A poll of 100 people is taken and they are asked whether they voted WTP. a What is the mean and standard deviation for this poll? b What is the probability that in the sample, the number of WTP voters lies within half a standard deviation of the mean?
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