Question

The first two questions refer to the following information:

Researchers developed an online tool to help ESL students learn prepositions and metaphors. A study measuring academic success in ESL students randomly sampled 100 Spanish speaking ESL students using traditional ESL classes and the new language tool and 81 Portuguese speaking ESL students using traditional ESL classes and the new language tool, and scored them on a common English fluency scale (higher score representing greater degree of fluency). The researchers suspected that the mean fluency score for Spanish speaking ESL students using the new language tool is higher than for Portuguese speaking students because the language platform has collected more data from Spanish speaking students on their platform and has tailored their curriculum towards these students. They wanted to check whether data would support this hypothesis.

Question 1 of 9

If μ₁ and μ₂ represent the mean fluency score for Spanish speaking and Portuguese speaking students respectively, which of the following is the appropriate pair of hypotheses in this case?

  Ho:μ1−μ2=0Ha:μ1−μ2<0Ho:μ1-μ2=0Ha:μ1-μ2<0

  Ho:μ1−μ2>0Ha:μ1−μ2=0Ho:μ1-μ2>0Ha:μ1-μ2=0

  Ho:μ1−μ2<0Ha:μ1−μ2=0Ho:μ1-μ2<0Ha:μ1-μ2=0

  Ho:μ1−μ2=0Ha:μ1−μ2>0Ho:μ1-μ2=0Ha:μ1-μ2>0

Ho:μ1−μ2=0Ha:μ1−μ2≠0Ho:μ1-μ2=0Ha:μ1-μ2≠0

Ho:μ1=μ2Ha:μ1≠μ2Ho:μ1=μ2Ha:μ1≠μ2

Question 2 of 9

Researchers developed an online tool to help ESL students learn prepositions and metaphors. A study measuring academic success in ESL students randomly sampled 100 Spanish speaking ESL students using traditional ESL classes and the new language tool and 81 Portuguese speaking ESL students using traditional ESL classes and the new language tool, and scored them on a common English fluency scale (higher score representing greater degree of fluency). The researchers suspected that the mean fluency score for Spanish speaking ESL students using the new language tool is higher than for Portuguese speaking students because the language platform has collected more data from Spanish speaking students on their platform and has tailored their curriculum towards these students. They wanted to check whether data would support this hypothesis.

The following is the output for the t-test:
T-value: -2.10
P-Value: .02

Using a significance level of .05, what conclusion would you make

The data do provide sufficient evience that the mean fluency score for Spanish speakers is not different than that of Portuguese speakers.

The data do not provide sufficient evidence that the mean fluency score for Spanish speakers is larger than that of Portuguese speakers.

The data do not provide sufficient evidence that the mean fluency score for Spanish speakers is not different than that of Portuguese speakers so we accept the null hypothesis.

The data do provide sufficient evidence that the mean fluency score for Spanish speakers is larger than that of Portuguese speakers.

Researchers developed an online tool to help ESL students learn prepositions and metaphors. A follow up study measuring academic success in ESL students randomly sampled 100 ESL students and tested them before using the tool and then re-tested them after using the language tool on a common English fluency scale (higher score representing greater degree of fluency). The researchers suspected that the mean fluency score for each student would improve after using the new language tool. They wanted to check whether data would support this hypothesis.

Question 3 of 9

Given the design of the study and the questions of interest, which of the following 4 tests is relevant?

Paired T-Test

Two Sample T-Test

ANOVA

Chi-square

The next three questions refer to the following information:

Researchers developed an online tool to help ESL students learn prepositions and metaphors. A follow up study measuring academic success in ESL students using different study strategies.

Suppose three different groups were randomly selected and assigned to the following conditions:

• Control Group: Traditional ESL class only
• Self-Paced Group: ESL class with the option to use the tool at their own pace
• Course-Guided: ESL class with content assigned to use the tool regularly throughout the course

The means and standard deviations of the resulting English fluency scores from this hypothetical study are summarized below:

	nn	x¯x¯	ss
Group 1 (control)	30	98	2.3
Group 2 (self-paced)	30	115	4.1
Group 3 (course-guided)	32	103	3.2

Question 4 of 9

If we let μ₁, μ₂, and μ₃ be the mean fluency scores for groups 1, 2, and 3 respectively, the appropriate hypotheses in this case are:

  Ho:μ1=μ2=μ3Ha:μ1≠μ2≠μ3Ho:μ1=μ2=μ3Ha:μ1≠μ2≠μ3

  Ho:μ1≠μ2≠μ3Ha:μ1=μ2=μ3Ho:μ1≠μ2≠μ3Ha:μ1=μ2=μ3

  Ho:μ1=μ2=μ3Ha:μ1, μ2, μ3  are not all equalHo:μ1=μ2=μ3Ha:μ1, μ2, μ3  are not all equal

Ho:μ1, μ2, μ3  are not all equalHa:μ1=μ2=μ3Ho:μ1, μ2, μ3  are not all equalHa:μ1=μ2=μ3

Question 5 of 9

One of the conditions that allows us to use ANOVA safely is that of equal (population) standard deviations. Can we assume that this condition is met in this case?

No, since the population standard deviations are not given so we cannot check this

Yes, since 4.12.3≈1.78<24.12.3≈1.78<2

No, since the three sample standard deviations are not all equal

Yes, since 4.1 - 2.3 < 2

Question 6 of 9

An Analysis of Variance yielded the following results:
F-Value: 12.5
P-Value: .0000

Using a significance level of .05 interpret the results.

The data provides strong evidence that test scores are related to study strategy indicating that not all of the means are the same: one or more pairs have a statistically significant difference.

The data do not provide sufficient evidence that test scores are related to study strategy indicating that all of the means are the same: none have a statistically significant difference.

The data provides strong evidence that test scores are related to study strategy in the following way: the self paced group significantly outperformed the course guided group and the course guided group in turn out-performed the control group.

Question 7 of 9

A study was conducted on twins at age 6 months. One twin was assigned to be breastfed and another twin was assigned to be formula fed for the next 1.5 years. At the end of the two years, they conducted a battery of health tests and scored the toddlers for overall health with a total of 100 points, higher scores indicating greater health.

What hypothesis testing technique should the researcher use to analyze the data?

ANOVA

Paired T-Test

Two Sample T-Test

Chi-square

Question 8 of 9

In a study on pain, researchers randomly assigned participants to one of three conditions and asked them to hold an ice cube for as long as possible:

• Control Group: no pain management strategy offered
• Medication: Advil provided prior to task
• Profanity: Participants urged to yell profanities to deal with the pain

The time is recorded in seconds to determine how long each group can withstand the pain.

What hypothesis testing technique should the researcher use to analyze the data?

ANOVA

Paired T-Test

Two Sample T-Test

Chi-square

Question 9 of 9

A researcher wants to test how many power poses men do compared to women in one hour business presentations. The study randomly selects 30 men and 30 women in management level business meetings and analyze their recorded meetings to find the average number of power poses per meeting for each group.

Which of the following should the researcher use to determine whether there is a difference in mean number of power poses per meeting between men and women?

two-sample t-test

paired t-test

z-test for the population mean

ANOVA

Answer 1

As per Chegg guidelines we should answer only the first four sub parts of the question. But I have answered first six questions

Question 1

Ho:μ1−μ2=0 Ha:μ1−μ2>0

Question 2

As p-value<alpha=0.05 so,

The data do provide sufficient evidence that the mean fluency score for Spanish speakers is larger than that of Portuguese speakers.

Question 3

ANOVA

Question 4

Ho:μ1=μ2=μ3 Ha:μ1, μ2, μ3  are not all equal

Question 5

Yes, since 4.1 - 2.3 < 2

Question 6

As P-Value: .0000< alpha =0.05 so we reject H0 and conclude that,

The data provides strong evidence that test scores are related to study strategy indicating that not all of the means are the same: one or more pairs have a statistically significant difference.