1. A hypothesis test returns a p-value of 0.06 against the null hypothesis: The

Question

1. A hypothesis test returns a p-value of 0.06 against the null hypothesis: The identification of an elementary student as"gifted" is independent of their identification as dyslexic. What is a correct interpretation of this p-value? a) Only 6% of dyslexic students are identified as "gifted". b) Elementary students with dyslexia are only identified as "gifted" 96% as often as their non- dyslexic peers c) There is a 94% chance that dyslexia is independent from whether an elementary student is identified as "gifted". d) If dyslexia is independent from whether an elementary student is identified as "gifted", we would get a result indicating at least this much connection between the two 6% of the time e) None of these is a correct interpretation of the p value 2. A sales manager would like to know whether the male or female employees at her company are more likely to have a larger average number of sales. The manager does not know the population standard deviation. Which test statistic would be most appropriate to use in this hypothesis test? (Pi-P2)-(p-P) c) z= 3. A school district equity officer wants to test the null hypothesis that dyslexia is independent of whether an elementary student is identified as "gifted". Which test statistic would be most appropriate to use in the hypothesis test? X-2) ,(rows-1)(col-1) c) z= , l. n l 4. A politician wants to know whether the level of support for a certain ballot initiative is higher among Republicans than Democrats. Which test statistic would be most appropriate to test this hypothesis? :

Explanation / Answer

Solution to Question 1: Correct answer - (d).

Explanation: General interpretation of p-value is following:

" Under the assumption that null hypothesis H0 is true, out of 100 replications of the data observation set, there will be total of about (100*p-value) replications in which we will observe the test-statistic value more extreme than what we have observed with this particular dataset observation."

In our particular scenario, paraphrasing the statement "under the assumption that null hypothesis Ho is true" would give us "If dyslexia is independent from whether an elementary student is identified as "gifted" ". The test statistic in our case , would be some measure of dependency between an elementary student's identity as "gifted" vs dyslexia student.

Therefore, obtaining a specific p-value implies that (p-valur)*100% of the time, we will observe atleast as much dependency between "gifted" identity and "dyslexia" identity, as we have observed with current dataset.

Note that among all the given options, only option (d) has expilicitly mentioned the statement that "under the assumption that null hypothesis is true" . No other option has mentioned it. So this is sufficient to eliminate all other options.

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