Assignment #2_ Ch10, 12-question 8

1/27/24, 12:53 AM Assignment #2: Ch10, 12-Diatra Serra https://tdx.acs.pearsonprd.tech/api/v1/print/highered 1/2 Student: Diatra Serra Date: 01/27/24 Instructor: Victor Law Course: 202410 BUSN 3431 050 Assignment: Assignment #2: Ch10, 12 Consider the following hypothesis statement using 0.02 and the following data from two independent samples. Complete parts a and b below. = H : p − p ≤ 0.20 0 1 2 x 1 = 265 x 2 = 198 H : p − p > 0.20 1 1 2 n 1 = 300 n 2 = 250 a. Calculate the appropriate test statistic and interpret the result. The test statistic is based on the difference between two sample proportions . It can be found by using technology or the formula below, where x 1 is the number of observations of interest in sample 1, n 1 is the size of sample 1, p 1 is the proportion of observations of interest in population 1, x 2 is the number of observations of interest in sample 2, n 2 is the size of sample 2, p 2 is the proportion of observations of interest in population 2, and is the pooled estimate of the population proportion of observations of interest. z p − p 1 p 2 p with , , and z p = p 1 − p 2 − p 1 − p 2 H 0 p 1 − p 1 n 1 + 1 n 2 p = x 1 + x 2 n 1 + n 2 = p 1 x 1 n 1 = p 2 x 2 n 2 For this problem, use the formula. Calculate , rounding to four decimal places. p p = x 1 + x 2 n 1 + n 2 p = 265 + 198 300 + 250 p = 0.8418 Calculate the sample proportion, , rounding to four decimal places. p 1 p 1 = x 1 n 1 p 1 = 265 300 p 1 = 0.8833 Calculate the sample proportion, . p 2 p 2 = x 2 n 2 p 1 = 198 250 p 1 = 0.7920 Now substitute the known values into the formula to find , rounding to four decimal places. z p z p = p 1 − p 2 − p 1 − p 2 H 0 p 1 − p 1 n 1 + 1 n 2 z p = (0.8833 − 0.7920) − (0.20) 0.8418( ) 1 − 0.8418 1 300 + 1 250 z p = − 3.4783 The test statistic follows the normal distribution. Critical values are based on the test's significance level and determine the boundary for the rejection region. While technology or a table of cumulative normal distribution probabilities could be used to find the critical value, in this problem, use technology. Determine the critical value for 0.02, rounding to four decimal places. =