1. Your classmates were invited to complete a survey. One of the survey questions was, "Math anxiety is described as feeling stressed and anxious when doing math. How would you rate your math anxiety?" Students could choose to respond with a level from 1 to 5, where level 1 means very low math anxiety and level 5 means very high math anxiety. See the Excel sheet "Assignment 5 - Survey" given in in the "Written Assignment 5" folder on Sakai for the responses.

a) Before you complete any inferences on the sample data, you should first summarize the survey results in a frequency distribution table. Use Excel to sort or filter the data so that you can get a count for each category.

Sort the math anxiety level data using the following steps: Select all the cells in the header row. In this sheet, you would select cells A1 to B1.

Click the Data tab in the top menu and click Filter.

Click the triangle beside the header called Math Anxiety Level and click Sort Smallest to Largest.

Now, you will see all the math anxiety levels arranged from 1 to 5. You can use the triangle button again to filter each level to get a frequency count in the bottom left corner of your sheet. Or, you can highlight the desired cells and look at the bottom right corner of your sheet for the count. Omit any responses which are blank.

For this part, submit only the completed frequency distribution table. (Hint: One frequency count is already completed for you.)

Math Anxiety Level	Frequency
1	18
2
3
4
5

b) Let represent the proportion of all STAT/MATH 1F92 students who have very high math anxiety, meaning they responded with a math anxiety level of 5. Use your summarized results from part a) to find a point estimate for p.

c) Find a 98% confidence interval for the proportion of STAT/MATH 1F92 students who have very high math anxiety.

d) If more than 10% of students enrolled in the course express feelings of very high math anxiety, then the department plans to offer additional math support workshops next year. Based on your confidence interval from part c), do you recommend that action needs to be taken? Explain.

e) Is there evidence to suggest that the proportion of STAT/MATH 1F92 students who have very high math anxiety is greater than 0.10? Use a significance level of = 0.01. Use the critical value method and show all six steps for hypothesis testing.

f) Compare your confidence interval result from part c) with your hypothesis testing result from part e). Are these results consistent with each other? Explain.

g) The department is interested in conducting a similar survey next year for all students enrolled in a first-year statistics course. They want to be 95% confident that the estimate of the proportion of students with very high math anxiety is within 3 percentage points of the true proportion. Using this year's survey data as a prior estimate of the proportion, how many students should be surveyed next year?

2. Some experts believe that 20% of all freshwater fish in Canada have high levels of mercury that are dangerous for consumption. Suppose a fish market has 250 fish are tested and 58 of them have dangerous levels of mercury. Is there evidence to suggest that the proportion of fish with dangerous levels of mercury is different from 20%? Use a significance level of = 0.05.

a) Use the critical value method and show all six steps for hypothesis testing.

b) Use the p-value method and show all six steps for hypothesis testing. Check that you obtain the same conclusion as part a).

c) Identify and describe the type of error that may have been committed in this hypothesis test.