# Hypothesis testing

I was given this problem as homework and am confused on how to approach it

We want to know if a chemistry students gender is a statistically significant factor in predicting the average chemistry test score. The list below gives test scores by gender. These scores were taken from as a simple random sample from the population of all chemistry students

female: 59 77 95 98 82 83

male: 56 77 78 79 79 66 88 89 90 90

Do a hypothesis test to decide if the gender of the chemistry student is statistically significant for performance on a chem test. (alpha = 0.05)

• Hi mandy, welcome to Cross Validated. Thanks for being clear about the source of the question. We treat these routine bookwork questions a little differently (see the discussion in the help center near the word "Homework"). Please add the self-study tag, read its tag-wiki and modify your question to follow the guidelines on asking such questions. In particular, you'll need to clearly identify what you've done to solve the problem yourself, and indicate the specific help you need at the point you struck difficulty. – Glen_b Aug 20 '16 at 3:16
• Here is a general guide on t tests for difference in means. Try to solve it using this and if you're stuck show us some work and we can help. stattrek.com/hypothesis-test/… – VCG Aug 20 '16 at 3:18
• Note that it asks you to compare ("average chemistry test score" and that it mentions a "simple random sample of all students" (suggesting that the scores should be independent or close to it. – Glen_b Aug 20 '16 at 3:26
• I guess where I am stuck is should I be approaching this as a proportion hypothesis problem or a mean hypothesis testing problem. If I use the mean approach I think I should I take the average of all these values and find the mean x(bar)female=82.3 and x(bar)male=79.2 and then do a two tailed test with H0: mu(male)=mule(female) and Ha: mu(male) not equal to mu(female) – mandy Aug 20 '16 at 3:27
• questions like "If this was a proportions test, what would be the proportion?" are exactly the question to ask yourself when making these decisions. It looks like you already see that there isn't one here (though a small change to the question could make it one -- like if it became a question about pass rates, say) – Glen_b Aug 20 '16 at 4:20

The question you were asked is quite poorly worded; that doesn't help (in fact if a student wrote that way I'd be inclined to deduct marks for it). It seeks a test for a difference in means ("average chemistry test score"). The "simple random sample of all students" implies that the scores should be independent or close to it. Do you know of any tests for a difference in means with two independent samples?

• two sample t test? – mandy Aug 20 '16 at 3:36
• If that's the only one you know how to do, then that might well be the intent, I'd think. (Test scores are of course clearly non-normal, though in many cases this wouldn't be much of an issue.) – Glen_b Aug 20 '16 at 4:21

Proportion Test: Carryout a Chi-Square test by converting the chemistry score into two groups "High" and "Low". Give tag "High" to students ( irrespective of gender) who score greater than equal to mean score; similarly, give tag "Low" to students ( irrespective of gender" who score less than mean score.

mean_score = (59 + 77 + 95 + 98 + 82 + 83 + 56 + 77 + 78 + 79+ 79 + 66 + 88 + 89 +90 + 90)/16
mean_score = 80.375


Subsequently, you should be able to prepare a contingency table as given below:

         | High |  Low
Female      4      2
Male        4      6


Now conduct a Hypotheses test using Chi-square.

Null Hypotheses: Gender has no impact on chemistry score.
Alternate Hypotheses: Gender has impact on chemistry score.

• Testing this way loses power over say a t test of the difference between the two means. – Michael R. Chernick Jun 2 '19 at 17:13
• I suggest that your answer uses the data provided in the question without transformation. As it is, it seems to me that you're answering a different question. – Ertxiem - reinstate Monica Jun 2 '19 at 17:55