Question

Twelve (12) randomly selected adults were asked how many US states they had visited and how many foreign countries they had visited. Use α = .05 .

# of states, x     20 27 8 8 32 7 3 10 32 25 20 8

# of countries, y   0 5 0 7 5 5 0 5 10 4 4 8

Find the linear correlation coefficient, r. (Round to the nearest ten-thousandth.)

The heights and weights of 15 randomly selected adult men are shown in the table. Use α = .05 .

Ht (in.)    73  70  73  72  68  72  68  70  68  67  72  70  65  74  70

Wt (lbs.)  185 155 195 164 145 185 170 150 180 175 175 147 140 210 200

Find the linear correlation coefficient, r. (Round to the nearest ten-thousandth.)

The heights and weights of 15 randomly selected adult men are shown in the table. Use α = .05 .

Ht (in.)    73  70  73  72  68  72  68  70  68  67  72  70  65  74  70

Wt (lbs.)  185 155 195 164 145 185 170 150 180 175 175 147 140 210 200

Find the critical value. (Round to the nearest thousandth. If more than one value is found, enter the largest critical value.)

Answer 1

1. The linear correlation coefficient is r = 0.3173262

2. Let $\rho$ denotes the height and weight.

Let p denotes the true correlation coefficient between the two variables. To test null hypothesis H. :p =0 against alternative hypothesis H1 :p to Let r denotes the sample correlation coefficient between the two variables and n denotes the sample size. Here, p=0.6130, n = 15 The test statistic can be written as: trn - 2 V1 – 22 which under Ho follows a t distribution with n -2 df. We reject Ho at 0.05 level of significance if P-value < 0.050 or if tobs > t0.025,n–2 Now, The value of the test statistic = 2.797683 associated degrees of freedom = 13 The critical value == 2.160 P – value = P(|tn-2] > tobs) = 2 * P(t13 > 2.797683) = 2(1 – 0.992452) = 0.015097 Since p-value < 0.05 and tobs > tcritical = 2.160, so we reject H, at 0.05 level of significance Hence, we can conclude that there is a significant linear correlation between two variables