A new drug is being tested to see if it reduces the frequency of migraines. Study participants were divided into two groups. 49 participants in group 1 received
A new drug is being tested to see if it reduces the frequency of migraines. Study participants were divided into two groups. 49 participants in group 1 received the medication; 42 participants in group 2 received a placebo. After a period of six months, group 1 had a
Question a)
Let: μ1μ1 = the population mean number of migraines with the medication
μ2μ2 = the population mean number of migraines with the placebo
(Step 1) State the null and alternative hypotheses by selecting the appropriate symbol, and identify which tailed test:
H0:H0: μ1μ1 μ2μ2
H1:H1: μ1μ1 μ2μ2
Which tailed test you need to perform?
- two-tailed test
- right-tailed test
- left-tailed test
(Step 2) Find the critical value(s):
i) What value is the best criterion to decide which table to use?
- sample size
- standard deviation
- mean
ii) Which table (zortzort ) should be used?
- zz-table
- tt-table
iii) If you use zz-table, then state the closest left cumulative area in the table to find the critical value. If you use tt-table, then state 1 tail or 2 tails, αα value (in decimal) with the degrees of freedom, separated by a comma.
iv) State the critical value(s) : CV =
(Step 3) State the rejection region:
i) Select from the dropdown menu to shade to the left, to the right, between or left and right of the critical value(s); and then shade the rejection region(s). The arrow can only drag to the critical value(s) that is/are rounded to one decimal place (these values correspond to the tick marks on the horizontal axis).
Shade: . Click and drag the arrows to adjust the values.
ii) Reject H0H0 if test statistic value the critical value(s). (Select >< if outside of two CV or <> if between two CV.)
(Step 4) Calculate the test statistic:
i) Calculate the standard error which corresponds to the denominator of the test statistic (show 6 decimal places):
ii) Calculate the test statistic (rounded to 2 decimal places for z or 3 decimal places for t):
test statistic ==
(Step 5) Decision:
Since the test statistic is the critical value(s), we H0H0 at the αα= 0.01.
(Step 6) Conclusion : Interpret your decision above.
- There is not enough evidence to conclude that the medication reduces the participants' mean number of migraines.
- There is enough evidence to conclude that the medication reduces the population mean number of migraines.
- There is not enough evidence to conclude that the medication reduces the population mean number of migraines.
- There is enough evidence to conclude that the medication reduces the participants' mean number of migraines.
Question b)
i) Which type of error could have been made in your conclusion above?
ii) Explain the error in that situation.
- It could be a mistake to reject the null hypothesis when the medication actually raises or has no effect on the population mean number of migraines.
- It could be a mistake not to reject the null hypothesis when the medication actually reduces the population mean number of migraines.
- It could be a mistake not to reject the null hypothesis when the medication actually reduces the participants' mean number of migraines.
- It could be a mistake to reject the null hypothesis when the medication actually raises or has no effect on the participants' mean number of migraines.
- It could be a mistake to reject the null hypothesis when the medication actually reduces the population mean number of migraines.
- It could be a mistake not to reject the null hypothesis when the medication actually raises or has no effect on the population mean number of migraines.
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