Question

At a community college, the mathematics department has been experimenting with four different delivery mechanisms for content in their Statistics courses. One method is traditional lecture (Method I), the second is a hybrid format in which half the time is spent online and half is spent in-class (Method II), the third is online (Method III), and the fourth is an emporium model from which students obtain their lectures and do their work in a lab with an instructor available for assistance (Method IV). To assess the effective of the four methods, students in each approach are given a final exam with the results shown in the following table. Assume an approximate normal distribution for each method. At the 5% significance level, does the data suggest that any method has a different mean score from the others?

Method I

Method I	81	81	85	67	88	72	80	63	62	92	82	49	69	66	74	80
Method II	85	53	80	75	64	39	60	61	83	66	75	66	90	93
Method III	81	59	70	70	64	78	75	80	52	45	87	85	79
Method IV	86	90	81	61	84	72	56	68	82	98	79	74	82

(be very careful when inputting your data; triple check, if necessary)

Include all hypothesis test with all four steps that are clearly labeled

include confidence intervals with all outputs as well as the CI itself

include which calculator function is used for each problem.

Answer 1

The solution of details solve in MINITAB software given below

The four different methods of all combination is 6 two sample independent test we use to check the any method has a different mean score from the others.

Ho: There is no significance difference between the any two combination method has a diferent mean score from others.

H1: There is significance difference between the any two combination method has a diferent mean score from others.

1)

Two-Sample T-Test and CI: Method I, Method II

Method

μ₁: mean of Method I

µ₂: mean of Method II

Difference: μ₁ - µ₂

Equal variances are not assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Method I	16	74.4	11.3	2.8
Method II	14	70.7	15.1	4.0

Estimation for Difference

Difference	95% CI for Difference
3.72	(-6.46, 13.90)

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ ≠ 0

T-Value	DF	P-Value
0.76	23	0.457

The p-value =0.457 is greater than alpha value=0.05 (level of significance) then Accept Ho (null hypothesis)

Conclusion: There is no significance difference between the two combination Method-I and Method-II of mean score.

Interpretaion: There is no significance difference between the two combination traditional lecture and hybrid format method

2)

Two-Sample T-Test and CI: Method I, Method III

Method

μ₁: mean of Method I

µ₂: mean of Method III

Difference: μ₁ - µ₂

Equal variances are not assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Method I	16	74.4	11.3	2.8
Method III	13	71.2	12.9	3.6

Estimation for Difference

Difference	95% CI for Difference
3.28	(-6.11, 12.68)

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ ≠ 0

T-Value	DF	P-Value
0.72	24	0.478

The p-value =0.478 is greater than alpha value=0.05 (level of significance) then Accept Ho (null hypothesis)

Conclusion: There is no significance difference between the two combination Method-I and Method-III of mean score.

Interpretaion: There is no significance difference between the two combination traditional lecture and online method

3)

Two-Sample T-Test and CI: Method I, Method IV

Method

μ₁: mean of Method I

µ₂: mean of Method IV

Difference: μ₁ - µ₂

Equal variances are not assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Method I	16	74.4	11.3	2.8
Method IV	13	77.9	11.6	3.2

Estimation for Difference

Difference	95% CI for Difference
-3.49	(-12.29, 5.32)

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ ≠ 0

T-Value	DF	P-Value
-0.82	25	0.422

The p-value =0.422 is greater than alpha value=0.05 (level of significance) then Accept Ho (null hypothesis)

Conclusion: There is no significance difference between the two combination Method-I and Method-IV of mean score.

Interpretaion: There is no significance difference between the two combination traditional lecture and emporium model method

4)

Two-Sample T-Test and CI: Method II, Method III

Method

μ₁: mean of Method II

µ₂: mean of Method III

Difference: μ₁ - µ₂

Equal variances are not assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Method II	14	70.7	15.1	4.0
Method III	13	71.2	12.9	3.6

Estimation for Difference

Difference	95% CI for Difference
-0.44	(-11.57, 10.69)

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ ≠ 0

T-Value	DF	P-Value
-0.08	24	0.936

The p-value =0.936 is greater than alpha value=0.05 (level of significance) then Accept Ho (null hypothesis)

Conclusion: There is no significance difference between the two combination Method-II and Method-III of mean score.

Interpretaion: There is no significance difference between the two combination methods hybrid format and online model method

5)

Two-Sample T-Test and CI: Method II, Method IV

Method

μ₁: mean of Method II

µ₂: mean of Method IV

Difference: μ₁ - µ₂

Equal variances are not assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Method II	14	70.7	15.1	4.0
Method IV	13	77.9	11.6	3.2

Estimation for Difference

Difference	95% CI for Difference
-7.21	(-17.86, 3.44)

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ ≠ 0

T-Value	DF	P-Value
-1.40	24	0.175

The p-value =0.175 is greater than alpha value=0.05 (level of significance) then Accept Ho (null hypothesis)

Conclusion: There is no significance difference between the two combination Method-II and Method-IV of mean score.

Interpretaion: There is no significance difference between the two combination methods hybrid format and emporium model model method

6)

Two-Sample T-Test and CI: Method III, Method IV

Method

μ₁: mean of Method III

µ₂: mean of Method IV

Difference: μ₁ - µ₂

Equal variances are not assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Method III	13	71.2	12.9	3.6
Method IV	13	77.9	11.6	3.2

Estimation for Difference

Difference	95% CI for Difference
-6.77	(-16.71, 3.17)

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ ≠ 0

T-Value	DF	P-Value
-1.41	23	0.172

The p-value =0.172 is greater than alpha value=0.05 (level of significance) then Accept Ho (null hypothesis)

Conclusion: There is no significance difference between the two combination Method-II and Method-IV of mean score.

Interpretaion: All the combination of different method does the data suggest that any method has a different mean score from the others at the 5% significance level,

Interpretaion: There is no significance difference between the two combination methods online and emporium  model method