 # Introduction to Statistics

## Transcribed Text

Question 1 A country report claims that the mean monthly expenses for a family of 4 is US\$2,500 per month. You believe that the mean cost is more than US\$2,500 per month. You randomly selected a sample of 300 families of 4 and found out the mean cost is US\$2,750 with a standard deviation of \$350. Assuming that the population is normally distributed, test, at the 10% level of significance, whether the report is underestimating the mean monthly expenses for a family of 4, by answering the following: (a) State the null and alternative hypotheses for the test. (b) Calculate the test statistics. (c) Determine the rejection region(s) for the test. (d) State the conclusion for the test giving reasons for your answer. Question 2 Six months after graduating from college, randomly selected graduates were surveyed to determine their level of job pressure. The data was inputted into MINITAB Version 17.0 for analysis to determine whether level of job pressure is independent of gender. The following output, Exhibit 1, was generated using MINTAB: Page 29 of 31 Exhibit 1 Chi-Square Test for Association: Age (years), Degree of Job Pressure Rows: Age (Years) Columns: Degree of Job Pressure Low Medium High All Less than 20 22 18 24 64 20.84 21.58 * 0.06424 0.59346 0.27173 20 - 39 52 48 46 146 47.55 49.23 49.23 0.41687 0.03054 ** 40 - 59 60 65 61 186 60.57 62.71 62.71 0.00545 0.08343 0.04677 60 and Above 36 45 45 126 41.03 42.48 42.48 0.61768 0.14915 0.14915 All 170 176 176 522 Cell Contents: Count Expected count Contribution to Chi-square Chi-Square = 2.640, DF = ***, P-Value = 0.852 (a) State the null and alternative hypotheses for the test. (b) Determine the missing values “*”, “**” and “***”. (c) State the conclusion for the test giving reasons for your answer.

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2)

A) H₀:μ₁=μ₂=μ₃=μ₄;
Ha:μ₁≠μ₂≠μ₃≠μ₄

B) The summation of the expected counts for this test are approximately equal to the summation of the counts for each row. So for *: 20.84+21.58+*=64, where *=21.58.

The summation of the contributions to Chi-square can be calculated to find the missing value. So for **: .06424+.59346+.27173+.41687+.03054+**+.00545+.08343+.04677+.61768+.14915+.14915=2.64, where **=.21153...
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