Question

Asked Apr 15, 2019

62 views

Given to dependent random samples with the following results:

Population 1: 83,72,64,61,72,74,72,66

Population 2: 85,64,66,52,78,83,70,68

Can it be concluded, from this data, that there is a significant difference between the two population means?

Let d= ( population 1 entry)-( population 2 entry), use a significance level of a = 0.05 for the test. Assume that both population are normally distributed.

1. State the null and alternative hypothesis for the test.

2. Find the value of the standard deviation of the paired differences. Round to one decimal place.

3. Commute the value of the test statistic. Round to three decimal places.

4. Determine the decision rule for rejecting the null hypothesis Ho. Round the numerical portion of your answer to three decimal places.

Step 1

Two dependent random samples are selected from a population and it is assumed that both populations are normally distributed. The level of significance for the test is α = 0.05.

The hypothesis test based on the data would be called a *paired comparisons test.* The difference between the pair of measurements is called *d _{i}*.

Step 2

**Part (1): Null and alternative Hypothesis for the test:**

Denote *μ _{1}* as the true mean of population 1 and

Let *μ _{d}* denote the difference between means of population 1 and population 2. That is,

*μ _{d }*=

The hypotheses appropriate for the test are as follows:

*Null hypothesis:*

*H*_{0}: *μ _{d }*=

*Alternate hypothesis:*

*H*_{1}:* μ _{d }*≠

Step 3

**Part (2): Finding the value of the standard deviation of the paired differences:**

The difference between each pair observations is obtained as,

di = population 1 entry – population 2 entry for the i’th pair of observations.

In Excel, put population 1 data in column A and population 2 data in column B, without using column headings so that first pair of data is on line 1.

In cell C1, enter the formula, =A1 – B1. This calculates the difference, di, for t...

Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: You receive a brochure from a large university. The brochure indicates that the mean class size for...

A: According to the given question, to test the claim that The brochure indicates that the mean class s...

Q: Previously, you studied linear combinations of independent random variables. What happens if the var...

A: Hey, since there are multiple subpart questions posted, we will answer first three subparts. If you ...

Q: . A tire manufacturer claims that the mean life of a certain type of tire is more than 30,000 miles....

A: The claim is provided as that the mean, life of a certain type of tire is more than 30,000 miles.a...

Q: Five children aged 2, 3, 5, 7 and 8 years old weigh 14, 20, 32, 42 and 44 kilograms respectively. Fi...

A: Let x be the age of children and y be the weight of children.The equation of the regression line is:

Q: At wind speeds above 1000 centimeters per second (cm/sec), significant sand-moving events begin to o...

A: (a) Calculation of confidence interval:The 95% confidence interval (CI) of the sample mean for a lar...

Q: A researcher wants to test to see if husbands are significantly older than their wives. To do this, ...

A: The aim is to find the accurate statement from the following options to evaluate the population mean...

Q: BASED ON THIS DATA, what does the r^2 values tell you? and the linear regression line is the inform...

A: Note:Hi there! Thank you for posting the question! However, the circumstances of the study presented...

Q: Describe the main difference between a dependent and an independent t test. (Note: I am not asking y...

A: Dependent t-test: The dependent t-test, also known as the “paired t-test”, is a statistical procedur...

Q: Professor Jennings claims that only 35% of the students at Flora College work while attending school...

A: (a) Level of significance:It is given that to test whether more than 35% of the students have jobs, ...