Question

Question 1 1 pts

(The following research scenario is the basis for all the questions in this assignment.)

According to a Gallup survey from 2013, Americans sleep an average of 6.8 hours per night. I was curious whether sleep time is significantly different now (2018) compared to 2013. So I measured the sleep of 16 different people over a week, and came up with an average score for each person. I assume that the sleep time among all Americans is normally distributed, and I set the significance level at α = .05.

Identify the dependent variable (DV) and the independent variable (IV, which differentiate the two populations being compared)

Group of answer choices

DV-Sleep; IV-Year

DV-Year; IV-Sleep

DV-2013; IV-Sleep

DV-Hours of sleep per night; IV-Year

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Question 2 1 pts

A hypothesis test is based on the probability of the null hypothesis being true, so it is the null hypothesis that is being "tested." What is the null hypothesis in this research scenario? Remember that the researcher in this case does not predict a particular direction for the difference between 2013 and 2018 in terms of hours slept per night, so the null hypothesis should also reflect this non-directional approach.

Group of answer choices

There is no significant difference in hours slept per night between 2013 and 2018.

There is no significant difference between hours slept per night and year.

There is a significant difference between hours slept per night and year.

There is a significant difference in hours slept per night between 2013 and 2018.

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Question 3 1 pts

The notation for the alternative hypothesis for this research scenario is ______.

Group of answer choices

µ₂₀₁₈ ≠ µ₂₀₁₃

µ ₂₀₁₈= µ₂₀₁₃

µ₂₀₁₈ > µ₂₀₁₃

µ ₂₀₁₈ < µ₂₀₁₃

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Question 4 1 pts

The comparison population is represented by the national statistics from 2013 with a population mean of 6.8 hours of sleep per night. The population standard deviation is not provided so it needs to be estimated from the sample. The population mean is estimated with the sample mean. Use the sample data below to calculate the sample mean (estimated population mean) and the estimated population standard deviation.

Subject	Hours slept per night
1	5
2	7
3	6
4	8
5	5
6	6
7	7
8	5
9	8
10	9
11	6
12	7
13	4
14	6
15	7
16	8

Group of answer choices

mean = 6.5; standard deviation = 1.37

mean = 6.5; standard deviation = 1.32

mean = 6.5; standard deviation = 1.39

mean = 6.5; standard deviation = 1.18

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Question 5 1 pts

Because the sample mean (from data for current hours of sleep per night I collected) needs to be compared to a distribution of all possible sample means (i.e., the sampling distribution), calculate the standard error (standard deviation of the sampling distribution) from the estimated population standard deviation that you just calculated in the previous question.

Group of answer choices

.42

.34

.33

.09

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Question 6 1 pts

When the comparison population (2013 hours slept per night) has a known mean (μ) but no known standard deviation (σ), we use the sample to estimate the population standard deviation and then convert the population into a t distribution. This means we are conducting a t test and we need to calculate the t statistic for our sample to see where it is located on the sampling distribution. Use the information from the research scenario and the previous questions to calculate the t statistic. (Round the answer to 2 decimal places.)

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Question 7 1 pts

Now that we know where the sample mean t statistic is located on the t sampling distribution, the next step is to find out whether the t statistic falls into the significant region. Identify the critical t value(s) in the following choices. As a reminder, I (the researcher) want to know if the hours slept per night now are significantly different from the hours slept per night in 2013, and I do not predict any direction of the potential difference. Use significance level α = .05.

Group of answer choices

2.306, -2.306

2.132, -2.132

-1.86

2.132

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Question 8 1 pts

Comparing the t statistic with the critical t value(s), what is the hypothesis test result?

Group of answer choices

Reject the null hypothesis because the calculated t statistic is more extreme than the critical t value.

Reject the null hypothesis because the calculated t statistic is less extreme than the critical t value.

Fail to reject the null hypothesis because the calculated t statistic is less extreme than the critical t value.

Fail to reject the null hypothesis because the calculated t statistic is more extreme than the critical t value.

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Question 9 1 pts

Based on the hypothesis test result above, what is the correct answer to the research question?

Group of answer choices

Hours slept per night in 2018 is significantly different from hours slept per night in 2013.

Hours slept per night in 2018 is not significantly different from hours slept per night in 2013.

Hours slept per night in 2018 is not significantly lower than hours slept per night in 2013.

Hours slept per night in 2018 is significantly lower than hours slept per night in 2013.

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Question 10 1 pts

The hypothesis test result only tells us whether there is a significant different between the two populations or not, but not how much of a different there is. Calculate the standardized effect size for this test. (Round the answer to 2 decimal places).

Answer 1

The dependent variable (DV) and the independent variable (IV) are

DV-Hours of sleep per night; IV-Year

The null hypothesis is,

There is no significant difference in hours slept per night between 2013 and 2018.

The notation for the alternative hypothesis for this research scenario is ______.

µ₂₀₁₈ ≠ µ₂₀₁₃

as this is non-directional hypothesis test.

From the data,

= 6.5

SD = 1.37

mean = 6.5; standard deviation = 1.37

Standard error = SD / = 1.37 / = 0.3425

The answer is,

.34

Question 6 1 pts

t = ( - ) / Std error = (6.5 - 6.8) / 0.34 = -0.88

Degree of freedom = n-1 = 16-1 = 15

Critical value of t at = 0.05 and df = 15 are,

2.132, -2.132

Since the test statistic (-0.88) lie between -2.132 and 2.132

Fail to reject the null hypothesis because the calculated t statistic is less extreme than the critical t value.

Since we fail to reject the null hypothesis,

Hours slept per night in 2018 is not significantly different from hours slept per night in 2013.

Effect Size = | - | / SD = | 6.5 - 6.8| / 1.37 = 0.22