Names ______

BA 253: ICE 9

1) Are women neater than men? One hundred FLC students were asked how many times they cleaned their bathrooms (during a month) and the results are in the table below. At α = 2%, do women clean more often than men? List the null and alternative hypotheses, calculate the test statistic and determine the p-value. Considering the zstat and the p-value, would you say that the statistical evidence is compelling, very compelling, or extremely compelling that women are neater than men? [Note: What kind of HT is this? Which function on your calculator will solve it?]

Women / Men
n / 54 / 46
/ 3.5 / 1.3
s / 1.5 / 1.2

2) Use the data collected in class, for the question determined in class, sorted by gender. Is there statistical evidence that the population proportion for males is different than for females? a) First, simply compare the sample proportion for each group, without doing any statistical analysis. Do the proportions seem to be about the same or do they appear significantly different? b) Now, perform the hypothesis test at α = 5%. Do you agree with the results of the hypothesis test? c) What does the p-value say about the plausibility of the null hypothesis?


3) So far, we have tested one mean, one proportion, two means and two proportions. The next step (perhaps obviously) is to test three or more means. This test is called an ANOVA test, with which we can determine in a single test whether several means are all similar (the same) or whether at least one of the means is significantly different than the rest. So the hypotheses for four means would be:

H0: µ1 = µ2 = µ3 = µ4

Ha: At least one µ is different.

This test may be relevant to determine if several products all have the same average at once or to determine if several different versions of an examination are fair – that is, have the same average.

To run this test, input your data into different lists on your calculator. Then find the ANOVA() function, and if you have four sets of data, run ANOVA(L1,L2,L3,L4) and determine the final result based on the p-value – interpret this the same way we always have.

Problem:

Three different brands of 40w lightbulbs have been tested to see how long they last. At α = 5%, do the three brands have the same lifespan are the lifespans different? a) Calculate the sample mean and sample standard deviation for each brand. Just by looking at these statistics, do they all appear to have approximately the same average? b) Run an ANOVA test on the data. Are the brands the same or different? c) Interpret the p-value regarding the plausibility of the null hypothesis. d) Can one brand make the claim that their lightbulbs last significantly longer than the other brands?

Brand A / Brand B / Brand C
224 / 141 / 245
138 / 140 / 215
104 / 312 / 268
172 / 290 / 275
204 / 365 / 205
301 / 384 / 254
207 / 186 / 197
223 / 306 / 252
334 / 357 / 283
269 / 251
282 / 248
249 / 297
231
359