The average final exam score for the statistics course is 77%. A professor wants to see if the average final exam score for students who are given colored pens on the first day of class is different. The final exam scores for the 14 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal.70, 65, 83, 90, 88, 69, 97, 100, 88, 79, 96, 83, 70, 96What can be concluded at the α = 0.01 level of significance?a. For this study, we should use [Select an answer]b. The null and alternative hypotheses would be:\[ H_0: \, ? \, \]\[ H_1: \, ? \, \]c. The test statistic = ______ (please show your answer to 3 decimal places.)d. The p-value = ______ (Please show your answer to 4 decimal places.)e. The p-value is [Select an answer]f. Based on this, we should [Select an answer]g. Thus, the final conclusion is that:- ○ The data suggest the population mean is not significantly different from 77 at α = 0.01, so there is statistically insignificant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is equal to 77.- ○ The data suggest the population mean is significantly different from 77 at α = 0.01, so there is statistically significant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is different from 77.- ○ The data suggest that the population mean final exam score for students who are given colored pens at the beginning of class is not significantly different from 77 at α = 0.01, so there is statistically insignificant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is different from 77.Hint: Helpful Videos: Calculations [link], Setup [link], Interpretations [link]

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Description: The average final exam score for the statistics course is 77%. A professor wants to see if the average final exam score for students who are given colored pens on the first day of class is different. The final exam scores for the 14 randomly selecte

Given Information: The average exam score for statistics course is 77% Sample size (n) = 14 To check if the average final exam score for students who are given colored pens on the first day of class is different: Significance level α= 0.01 Since, population standard deviation is not known, we use a t-test. State the Hypothesis as follows: Null Hypothesis: H0:μ=77 i.e., There is no significant difference (or) the average final exam score for students who are given colored pens on the first day is 77%. Alternative Hypothesis: Ha:μ≠77 i.e., here is a significant difference (or) the average final exam score for students who are given colored pens on the first day is different or not equal to 77%. The test statistic is given by the formula: t=x¯-μsn where, x¯ is the sample mean and s is the sample standard deviation. Calculation of Sample mean: x¯=70+65+83+90+.......70+9614=117414≈83.857 Calculation of sample standard deviation: s=70-83.862+65-83.862+......96-83.86214-1=11.72018≈11.7202 Substitute the values in the formula of the test statistic: t=x¯-μsn=83.857-7711.720214=6.8573.1324≈2.1891 Thus, the value of the test statistic is 2.189 P-value is the probability of obtaining the value of the test statistic or a value more extreme, assuming the null hypothesis is true. Degrees of freedom = n-1=14-1=13 Using Excel function "=T.DIST.2T(2.189,13)", p-value obtained is 0.047446 ≈0.0474 Since, p-value is greater than the significance level α i.e., 0.047 > 0.01, we fail to reject the null hypothesis. The data suggest that the population mean final score for students who are given colored pens at the beginning of class is not significantly different from 77 at 0.01 significance level, so there is statistically insignificant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is different from 77.

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The average final exam score for the statistics course is 77%. A professor wants to see If average score for students who are given colored pens on the first day of class is different. The final exam scores for the 14 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 70, 65, 83, 90, 88, 69, 97, 100, 88, 79, 96, 83, 70, 96 What can be concluded at the the a=0.01 level of significince level of significance?

The average final exam score for the statistics course is 77%. A professor wants to see If average score for students who are given colored pens on the first day of class is different. The final exam scores for the 14 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 70, 65, 83, 90, 88, 69, 97, 100, 88, 79, 96, 83, 70, 96 What can be concluded at the the a=0.01 level of significince level of significance?

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The average final exam score for the statistics course is 77%. A professor wants to see if the average final exam score for students who are given colored pens on the first day of class is different. The final exam scores for the 14 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal.

70, 65, 83, 90, 88, 69, 97, 100, 88, 79, 96, 83, 70, 96

What can be concluded at the α = 0.01 level of significance?

a. For this study, we should use [Select an answer]

b. The null and alternative hypotheses would be:

\[ H_0: \, ? \, \]

\[ H_1: \, ? \, \]

c. The test statistic = ______ (please show your answer to 3 decimal places.)

d. The p-value = ______ (Please show your answer to 4 decimal places.)

e. The p-value is [Select an answer]

f. Based on this, we should [Select an answer]

g. Thus, the final conclusion is that:

- ○ The data suggest the population mean is not significantly different from 77 at α = 0.01, so there is statistically insignificant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is equal to 77.

- ○ The data suggest the population mean is significantly different from 77 at α = 0.01, so there is statistically significant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is different from 77.

- ○ The data suggest that the population mean final exam score for students who are given colored pens at the beginning of class is not significantly different from 77 at α = 0.01, so there is statistically insignificant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is different from 77.

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