The following information was obtained from matched samples taken from two populations. Assume the population of differences is normally distributed. Individual :1 2 3 4 5;
Method 1: 7 5 6 7 5 ;
Method 2: 5 9 8 7 6.

The null hypothesis tested is H0: μd = 0. The test statistic for the difference between the two population means is:

a. 0.
b. 2.
c. -2.
d. -1

Correct option is d. -1.

Step-by-step explanation:

The dependent t-test (also known as the paired t-test or paired samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.

The hypothesis for the test can be defined as follows:

The test is given by:

Compute the differences as follows:

Individual       Method 1       Method 2       Difference (d = 1 - 2)

      1                      7                    5                        2

      2                     5                    9                       -4

      3                     6                    8                       -2

      4                     7                    7                         0

      5                     5                   6                         -1

Compute the sample mean and sample standard deviation of the differences as follows:

Compute the test statistic as follows:

Thus, the test statistic for the difference between the two population means is -1.

c = 0.429t

step-by-step explanation:

the constant rate at which carlos harvests cassava is 35 minutes per 15 cassavas 15/35 = 0.429 cassava per minute

therefore, an equation that models the number of cassava (c) that harvest carlos in a time (t) is the following:

where t is the time in minutes.

this means that when 35 minutes have elapsed 15 cassava have been harvested, at 70 minutes 30 cassava have been harvested and so on.