Question

Schools and museums: Do people who are interested in environment issues visit museums more often than people who are not? In 2012, the general social survey asked 1498 people how interested they were in environmental issues, and how often they had visited a science museum in the past year. The following table presents the results.

Number of Visits

None One More than one

Very Interested 513 138 58

Moderately Interested 459 98 34

Not Interested 163 20 15

Can you conclude that the number of visits to a science museum to interest in environmental issues? Use the a=0.05 level of significance and the P-Value method with the TI-84 Plus calculator.

(a) state the null and alternate hypotheses.

Ho: The number of visits to a science museum ________ related to interest in environmental issues.

H1: The number of visits to a science museum _______ related to interest in environmental issues.

Answer 1

The question of interest here is whether people exhibit interests in environmental issues, do visit science museums more often.

So basically, we are to determine if there is any relationship between the interest in environmental issues and museum visits. To do this, we shall use a Chi-square test.

The data provided for the same is:

	None	One	More than One	TOTAL
Very Interested	513	138	58	709
Moderately Interested	459	98	34	591
Not Interested	163	20	15	198
TOTAL	1135	256	107	1498

The number of rows here is n1 = 3 and the number of columns is n2 = 3. Hence, the degrees of freedom are:

The significance level is set at 0.05.

Using a Chi-square table, we get a critical value of 9.488.

Now, we begin determining the Chi-square statistic for the given table.

First, we compute the expected values. To do this, we multiply the total of each row and each column and divide this by the grand total.

For example, the expected value of very interested and none becomes:

Doing this, for all the cells, we get the expectation table as:

	None	One	More than One	TOTAL
Very Interested	537.1929	121.1642	50.6429	709
Moderately Interested	447.787	100.9987	42.2143	591
Not Interested	150.02	33.8371	14.1429	198
TOTAL	1135	256	107	1498

Next, we compute:

Doing so, we get:

	None	One	More than One
Very Interested	1.0895	2.3393	1.0688
Moderately Interested	0.2808	0.089	1.5984
Not Interested	1.1231	5.6584	0.0519

Now, the chi-square statistic is given by the formula:

Hence, summing all the values of the above table, we get:

Comparing this to the critical value, we have:

Hence, the ci-square statistic is greater than the critical value.

Therefore, we conclude at 0.05 significance level that there exists a relationship between the interest in environmental issues and the frequency with which people visit science museums.