Question

0 times a week - 32 students

1 time a week- 18 students

2 times a week - 29 students

3 times a week - 26 students

4 times a week - 33 students

5 times a week - 31 students

6 times a week - 27 students

7 times a week - 54 students

The data given shows how many times a week students drink caffeine. With this data, state the null and alternative hypothesis, calculate the test statistic and p-value, and calculate the confidence interval.

Answer 1

The Chi-Square test of independence is used to determine if there is a significant relationship between two factors.

For variables how many times a week and number of students ,

The Chi-Square test of independence is performed in following steps,

Step 1: The hypothesis is defined as,

Null hypothesis, Ho:There is no association between two variables.

Alternative hypothesis, Ha There is an association present between the two variables.

Step 2: The significance level for the test is,

Step 3: The Chi-Square test statistic is obtained as follow,

The observed values are,

	Drink Caffeine	Doesn't Drink 'k' times a week	Total
0 times a week	32	218	250
1 times a week	18	232	250
2 times a week	29	221	250
3 times a week	26	224	250
4 times a week	33	217	250
5 times a week	31	219	250
6 times a week	27	223	250
7 times a week	54	196	250
Total	250	1750

Step 4: The expected values are obtained using the formula,

The expected values are,

	Drink Caffeine	Doesn't Drink Caffeine	Total
0 times a week	31.25	218.75	250
1 times a week	31.25	218.75	250
2 times a week	31.25	218.75	250
3 times a week	31.25	218.75	250
4 times a week	31.25	218.75	250
5 times a week	31.25	218.75	250
6 times a week	31.25	218.75	250
7 times a week	31.25	218.75	250
Total	250	1750	2000

Step 5: Now the Chi-Square Value is obtained using the formula,

Step 4: The P-value for Chi-Square statistic is obtained using the chi square distribution table,

Step 5:

The null hypothesis is rejected. It can be stated now, the two variables are dependent. There is a statistically significant difference between how many times a week students drink caffeine.