Mathematics, 05.09.2020 23:01 katiemaley19

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

Answers: 3

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Answer from: CassidgTab

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:

$\text{H}_{0}:\mu_{d}=0\ \text{vs.}\ \text{H}_{\alpha}:\mu_{d}\neq0$

The test is given by:

$t=\frac{\bar d}{S_{d}/\sqrt{n}}$

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:

$\bar d=\frac{1}{n}\sum d=\frac{1}{5}\times [2-4-2+0-1]=-1\\\\S_{d}=\sqrt{\frac{1}{n-1}\sum (d-\bar d)^{2}}=\sqrt{\frac{1}{4}\times20}=2.2361$

Compute the test statistic as follows:

$t=\frac{\bar d}{S_{d}/\sqrt{n}}$

$=\frac{-1}{2.2361/\sqrt{5}}\\\\=-1$

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

Answer from: Quest

total amount to be paid = $19.5

step-by-step explanation:

given ,

original price = $25.99

discount = 25%

discount amount = 25% of original price

discount amount = 25/100 * 25.99

discount amount = $6.49

hence , the total amount to be paid = original price - discount amount

= $25.99 - $6.49

=$19.5

total amount to be paid = $19.5

Answer from: Quest

$5.41

step-by-step explanation:

$20 - $14.51 = $5.49.

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