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 there is a difference between the mean height of two cacti?
-Two-sample test for proportions
-Two-sample t-test
- Paired t-test
(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.
-The null hypothesis is not rejected. There is insufficient evidence of a difference between the mean height of two cacti.
-The null hypothesis is rejected. There is sufficient evidence of a difference between the mean height of two cacti.
-The null hypothesis is not rejected. There is sufficient evidence of a difference between the mean height of two cacti.
-The null hypothesis is rejected. There is insufficient evidence of a difference between the mean height of two cacti.
(e) Mark the correct statement at alpha = 0.05:
-The test result is statistically significant.
-The test result is not statistically significant.
(f) Explain the type of error, in context, that might have been made.
-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.
-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.
-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.
-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.
(g) What would the p-value have been if we had done a two-tailed test? (3 decimal places)

(f) 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.

What is sample statistics?

Any number calculated from your sample data is referred to as a sample statistic (or simply a statistic). The sample average, median, sample standard deviation, and percentiles are a few examples. Because a statistic is based on data obtained through random sampling, which is a random experiment, it is a random variable.

a) Since there are two independent samples and we want to compare population means. We must use: Two-sample t-test.

b) The value of the sample statistic to test those hypotheses is:

x1 bar - x2 bar = 12.1 - 11.2 = 0.9

c) This is two-tailed test. For p-value, use excel formula =TDIST(2.169,202,2).

p - value = 0.031

d) Since p-value is less than 0.05, correct option is:

The null hypothesis is rejected. There is sufficient evidence of a difference between the mean height of two cacti.

e) Since p-value is less than 0.05, correct option is:

-The test result is statistically significant.

f) Since null hypothesis is rejected, we might have been made Type I error. The correct option is:

-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.

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