Question

A horticulturist is studying the relationship between tomato plant height and fertilizer amount. Thirty tomato plants grown in similar conditions were subjected to various amounts of fertilizer (in ounces) over a four-month period, and then their heights (in inches) were measured. [You may find it useful to reference the t table.]

Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Fertilizer (ounces)	Height (inches)
1.7	20.5
6.0	49.8
4.3	56.1
1.2	24.5
4.2	29.2
5.3	60.5
3.2	24.2
0.0	25.4
2.1	26.2
2.6	25.4
0.8	26
3.0	28.8
4.6	62.8
3.3	30.3
5.5	43.1
2.1	33.3
3.0	35
1.6	22.2
3.8	40.7
6.0	44.8
3.8	29.8
0.5	21
1.7	25.2
2.4	29.8
4.4	27.6
3.1	32.7
4.0	33.3
0.0	22.6
2.3	27.2
3.5	46.6

Answer 1

We want to test if there is any relation between fertilizer and height of plant .

Hypothesis :

where rho is the population correlation coefficient .

Test statistic :

where r = sample correlation coefficient and n = sample size . and n =30 here .

We calculate using calculator : r = 0.739

So,  

Bonus : we found at alpha = 0.05 , df= 30-1=29  

Critical region :  

So, we reject the null hypothesis .

That is , there is strong relationship between the two variable