A scientist wants to determine whether or not the height of cacti, in feet, in Africa is significantly higher than the height of Mexican cacti. He selects random samples from both regions and obtains the following data.

Africa:

Mean = 12.1

Sample size = 201

Mexico:

Mean = 11.2

Sample size = 238

(a) Which of the following would be the correct hypothesis test procedure to determine if the height of cacti, in feet, in Africa is significantly higher than the height of Mexican cacti?

a. Paired t-test

b. Two-sample t-test

c. Two-sample test for proportions

(b) What is the value of the sample statistic to test those hypotheses?(2 decimal places)

(c) If the T test statistic is 2.169, and df = 202, find the p-value.(3 decimal places)

(d) Select the correct conclusion at alpha = 0.05.

a. The null hypothesis is rejected. There is sufficient evidence that African cacti are taller on average.

b. The null hypothesis is rejected. There is insufficient evidence that African cacti are taller on average.

c. The null hypothesis is not rejected. There is insufficient evidence that African cacti are taller on average.

d. The null hypothesis is not rejected. There is sufficient evidence that African cacti are taller on average.

(e) Explain the type of error, in context, that might have been made.

a. Type I error, which means the scientist concluded there is a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is no difference.

b. Type I error, which means the scientist concluded there is not a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is a difference.

c. Type II error, which means the scientist concluded there is a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is no difference.

d. Type II error, which means the scientist concluded there is not a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is a difference.

(f) What would the p-value have been if we had done a two-tailed test? (3 decimal places)