The data below give the lifetimes in hundreds of hours of samples of two types of electronic tubes. Past lifetime data of such tubes have shown that they can often be modeled as arising from a lognormal distribution. That is, the logarithms of the data are normally distributed. Assuming that variance of the logarithms is equal for the two populations, test, at the 5 percent level of significance, the hypothesis that the two population distributions are identical. Type 1 32, 84, 37, 42, 78, 62, 59, 74 Type 2 39, 111, 55, 106, 90, 87, 85

Proportion The proportion in some category is found by Proportions are also called relative frequencies, and we can display them in a relative frequency table. The proportions in a relative frequency table will add to 1 (or approximately 1 if there is some roundoff error). Relative frequencies allow us to make comparisons without referring to the sample size. One Categorical Variable Of the n=2625 people who responded to the survey, 735 agree with the statement that there is only one true love for each person, while 1812 disagree and 78 say they don't know. Table 2.1 displays these results in a frequency table, which gives the counts in each category of a categorical variable. Table 2.1 A frequency table: Is there one true