1 answer

The Office of Institutional Research at UP would like to examine the age distribution of the...

Question:

The Office of Institutional Research at UP would like to examine the age distribution of the student population. The office would like to determine whether the distribution of ages for a sample is different from the distribution of ages for the student population. A sample of students is selected and the relative frequencies for the age categories are as follows for the sample and the population: Age group: 18-20 Sample: Population: 27 a) State the null and alternative hypotheses in symbolic and text forms b) Compute the Chi-square. c) Draw conclusions at the 0.05 level of significance. 10· Over 30 21-24 42 30 29 18 26
The Office of Institutional Research at UP would like to examine the age distribution of the student population. The office would like to determine whether the distribution of ages for a sample is different from the distribution of ages for the student population. A sample of students is selected and the relative frequencies for the age categories are as follows for the sample and the population: Age group: 18-20 Sample: Population: 27 a) State the null and alternative hypotheses in symbolic and text forms b) Compute the Chi-square. c) Draw conclusions at the 0.05 level of significance. 10· Over 30 21-24 42 30 29 18 26

Answers

I have used Minitab software

Steps

  1. Enter the data   Worksheet 1 C1-T C2 C3 C4 C5 Сб Age 18-2021-24 25-29 over 30 1 sample 2 population 42 18 27 30 26 17
  2. Stat-table-Chi square test for association
  3.   Chi-Square Test for Association Summarized data in a two-way table Columns containing the table: 18-20 21-24 25-29 over 30 Labels for the table (optional) Rows: Age Columns: column (column with row labels) (name for column category) Select Statistics Options C14 Cancel Help OK
  4. ok

output

Welcome to Minitab, press Fl for help Chi-Square Test for Association: Age, column Rows: Age Columns: column over 18-20 21-24 25-29 30 All 18 22 sample 7 100 30 36 12 27 30 30 36 population 26 17 100 22 12 All 72 44 24 200 Count Expected count Cell Contents: Pearson Chi-Square 8.221, DF3, P-Value0.042 Likelihood Ratio Chi-Square= 8.370, DF= 3, P-Value= 0.039

.

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a)

The null hypothesis H0:Age distribution is same

The alternative hypothesis:H1:The age distribution is different

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b)Chi square=8.2

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c) As p-value is less than 0.05 we reject the null hypothesis and conclude that the age distribution of sample is different from age distribution of popuplation.

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THANK YOU

.

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