Question

To determine if there is a difference between the investing preferences of? mid-level managers working in the public and private sectors in a certain city. A random sample of 320 public-sector employees and 380 ?private-sector employees was taken. The sampled participants were then asked about their retirement investment decisions and classified as being either? "aggressive," if they invest only in stocks or stock mutual? funds, or? "balanced," if they invested in some combination of? stocks, bonds,? cash, and other. The results are available below. Complete parts a and b below.

	Aggressive	Balanced
Public	167	153
Private	234	146

Questions:

1) Use technology to calculate the test? statistic, rounding to two decimal places.

2) Use technology to calculate the? p-value, round three decimal places.

Please show work.

Answer 1

Answer Date: 01/04/2018 Test the claim that there is a difference between the investing preferences of mid-level managers working in the public and private sectors in a certain city at 5% level of significance The null and alternative hypothesis is, The null hypothesis is that there is no difference between the investing preferences of mid-level managers working in the public and private sectors in a certain city The alternative hypothesis is that there is a difference between the investing preferences of mid-level managers working in the publie and private sectors in a certain city. The chi-square test statistic of independence is, By using MINITAB software, find chi-square with help of following steps: 1) Import the data. 2) Select Chi-Square Test (Table in Worksheet) from Tables in Stat menu 3) Select Columns containing the table. 4) Click Ok.

Chi-Square Test: Aggressive, Balanced Expected counts are printed below observed counts Chi-Square contributions are printed below expected counts Aggressive Balanced Total 320 167 185.05 1.761 153 134.95 2.414 243 224.95 1.448 2 389 146 164.05 1.986 Total 410 299 709 Chi-Sq 7.609, DF# 1, P-value 0.006 From the MINITAB output, the chi-square test statistic of independence is7.61. The p-value is From the MINITAB output, the chi-square testp-value is 0.006 The p-value is 0.006

Decision The conclusion is that the significant p-value is less than 0.05 which is 0.006, so the null hypothesis is rejected at 5% level of significance. There is sufficient evidence to indicate that there is a difference between the investing preferences ofmid-level managers working in the public and private sectors in a certain city. The result is statistically significant.