Hypothesis Testing for Two Means and Two Proportions Quiz

PDF page 618: Two population means from independent samples where the population standard deviations are not known ̄ ̄

PDF page 618: • Distribution: Student’s t-distribution with degrees of freedom (variances not pooled)

PDF page 618: A hypothesis test of two population means from independent samples where the population standard deviations are known (typically approximated with the sample standard deviations) will have these characteristics: ̄ ̄

PDF page 618: • Distribution: normal distribution

PDF page 618: Test of two population proportions from independent samples ^ ^

PDF page 618: • Distribution: normal distribution

PDF page 618: • Random variable: X − X = the difference of the sampling means

PDF page 618: • Random variable: x = mean of the differences.

PDF page 618: • Distribution: Student’s t distribution with n – 1 degrees of freedom.

PDF page 618: • Samples are dependent.

PDF page 618: degrees of freedom (df) the number of objects in a sample that are free to vary pooled proportion estimate of the common value of p1 and p2 standard deviation a number that is equal to the square root of the variance and measures how far data values are from their mean; notation: s for sample standard deviation and σ for population standard deviation variable (random variable) a characteristic of interest in a population being studied. Common notation for variables are uppercase Latin letters X, Y, Z,... Common notation for a specific value from the domain (set of all possible values of a variable) are lowercase Latin letters x, y, z,.... For example, if X is the number of children in a family, then x represents a specific integer 0, 1, 2, 3, .... Variables in statistics differ from variables in intermediate algebra in two ways:

PDF page 619: c B A c ⎝n n ⎠ ⎣ B ⎦ A where the null hypothesis is H0: pA = pB or H0: pA – pB = 0 (p′ − p′ )

PDF page 634: 124. A new chocolate bar is taste-tested on consumers. Of interest is whether the proportion of children who like the new

PDF page 634: chocolate bar is greater than the proportion of adults who like it.

PDF page 620: 3. A new windshield treatment claims to repel water more effectively. Ten windshields are tested by simulating rain without

PDF page 620: the new treatment. The same windshields are then treated, and the experiment is run again. A hypothesis test is conducted.

PDF page 628: a. a test of two proportions

PDF page 628: College out of a total of 12,328 students. At Lake Tahoe College, there were 321 Hispanic students out of a total of 2,441 students. In general, do you think that the percent of Hispanic students at the two colleges is basically the same or different? Use the following information to answer the next three exercises. Neuroinvasive West Nile virus is a severe disease that affects a person’s nervous system. It is spread by the Culex species of mosquito. In the United States in 2010, there were 629 reported cases of neuroinvasive West Nile virus out of a total of 1,021 reported cases, and there were 486 neuroinvasive reported cases out of a total of 712 cases reported in 2011. Is the 2011 proportion of neuroinvasive West Nile virus cases more than the 2010 proportion of neuroinvasive West Nile virus cases? Using a 1 percent level of significance, conduct an appropriate hypothesis test.