Hypothesis Testing and Inferences

Hypothesis Testing and Inferences

Student’s Name

Institution Affiliation

Date

Table 3 (µ = 100 seconds and σ = 30)

Child Mean seconds of concentration in an experiment of reading z-score p-value
1 75 –0.83 0.203
2 81 –0.63 0.264
3 89 –0.37 0.356
4 99 –0.03 0.488
5 115 0.50 0.309
6 127 0.09 0.464
7 138 1.27 0.102
8 139 1.30 0.967
9 142 1.40 0.081
10 148 1.60 0.055

1st Question

Results from the standard normal table indicate that no child had come from a significantly different population (SDP) different from the one used in the null hypothesis. With consideration of the significant level of 0.05, all children had p-value greater than 0.05 (Silvey, 2017). These results would have been statistically significant if the null hypothesis was rejected under conditions that p < 0.05. In case, the p-value is greater than 0.05, and the null hypothesis would have been accepted since there is no enough evidence to reject the null hypothesis.

2nd Question

The significant level of each child becomes less at the same time with the progressive dispersion of data (Azzalini, 2017). This happens since there is a greater variation between variables.

Conclusion Statement

1st Student

The findings from the z analysis were to assess whether there was any child who appeared to come from a SDP that differed with the one used in the null hypothesis. Findings from z analysis show that the p-value is 0.203 at z < 0.83. As such, we accept the null hypothesis since p > 0.05.  

2nd Student

The findings from the z analysis were to assess whether there was any child who appeared to come from a SDP that differed with the one used in the null hypothesis. Findings from z analysis show that the p-value is 0.264 at z < 0.63. As such, we accept the null hypothesis since p > 0.05. 

3rd Student

The findings from the z analysis were to assess whether there was any child who appeared to come from a SDP that differed with the one used in the null hypothesis. Findings from z analysis show that the p-value is 0.356 at z < 0.37. As such, we accept the null hypothesis since p > 0.05. 

 

4th Student

The findings from the z analysis were to assess whether there was any child who appeared to come from a SDP that differed with the one used in the null hypothesis. Findings from z analysis show that the p-value is 0.488 at z <  0.03. As such, we accept the null hypothesis since p > 0.05. 

5th Student

The findings from the z analysis were to assess whether there was any child who appeared to come from a SDP that differed with the one used in the null hypothesis. Findings from z analysis show that the p-value is 0.309 at z <  0.50. As such, we accept the null hypothesis since p > 0.05. 

6th Student

The findings from the z analysis were to assess whether there was any child who appeared to come from a SDP that differed with the one used in the null hypothesis. Findings from z analysis show that the p-value is 0.464 at z < 0.09. As such, we accept the null hypothesis since p > 0.05. 

7th Student

The findings from the z analysis were to assess whether there was any child who appeared to come from a SDP that differed with the one used in the null hypothesis. Findings from z analysis show that the p-value is 0.102 at z < 1.27. As such, we accept the null hypothesis since p > 0.05. 

8th Student

The findings from the z analysis were to assess whether there was any child who appeared to come from a SDP that differed with the one used in the null hypothesis. Findings from z analysis show that the p-value is 0.0.967 at z < 1.30. As such, we accept the null hypothesis since p > 0.05. 

9th Student

The findings from the z analysis were to assess whether there was any child who appeared to come from a SDP that differed with the one used in the null hypothesis. Findings from z analysis show that the p-value is 0.081 at z < 1.40. As such, we accept the null hypothesis since p > 0.05. 

10th Student

The findings from the z analysis were to assess whether there was any child who appeared to come from a SDP that differed with the one used in the null hypothesis. Findings from z analysis show that the p-value is 0.055 at z < 1.6. As such, we accept the null hypothesis since p > 0.05.    

Table 4 (µ = 100 seconds and σ = 40)

Child Mean seconds of concentration in an experiment of reading z-score p-value
1 75 –0.63 0.264
2 81 –0.48 0.316
3 89 –0.28 0.390
4 99 –0.03 0.488
5 115 0.38 0.352
6 127 0.68 0.248
7 138 0.95 0.171
8 139 0.98 0.164
9 142 1.05 0.147
10 148 1.20 0.115

1st Question

The findings from the z-table analysis provide that no child that appeared to come from a SDP other than the one used in the null hypothesis (Silvey, 2017).

2nd

Level of significant for each child tends to reduce based on their variations.

 

Conclusion Statement

1st Student

The findings from the z analysis were to assess whether there was any child who appeared to come from a SDP that differed with the one used in the null hypothesis. Results from z analysis show that the p-value is 0.264 at z < 0.63. As such, we accept the null hypothesis since p > 0.05. 

2nd Student

The findings from the z analysis were to assess whether there was any child who appeared to come from a SDP that differed with the one used in the null hypothesis. Results from z analysis show that the p-value is 0.316 at z < 0.48. As such, we accept the null hypothesis since p > 0.05. 

3rd Student

The findings from the z analysis were to assess whether there was any child who appeared to come from a SDP that differed with the one used in the null hypothesis. Results from z analysis show that the p-value is 0.390 at z < 0.28. As such, we accept the null hypothesis since p > 0.05. 

4th Student

The findings from the z analysis were to assess whether there was any child who appeared to come from a SDP that differed with the one used in the null hypothesis. Results from z analysis show that the p-value is 0.352 at z < 0.38. As such, we accept the null hypothesis since p > 0.05. 

 

5th Student

The findings from the z analysis were to assess whether there was any child who appeared to come from a SDP that differed with the one used in the null hypothesis. Results from z analysis show that the p-value is 0.352 at z < 0.38. As such, we accept the null hypothesis since p > 0.05.

6th Student

The findings from the z analysis were to assess whether there was any child who appeared to come from a SDP that differed with the one used in the null hypothesis. Results from z analysis show that the p-value is 0.248 at z < 0.68. As such, we accept the null hypothesis since p > 0.05.

7th Student

The findings from the z analysis were to assess whether there was any child who appeared to come from a SDP that differed with the one used in the null hypothesis. Results from z analysis show that the p-value is 0.171 at z < 0.95. As such, we accept the null hypothesis since p > 0.05. 

8th Student

The findings from the z analysis were to assess whether there was any child who appeared to come from SDP that differed with the one used in the null hypothesis. Results from z analysis show that the p-value is 164 at z < 0.98. As such, we accept the null hypothesis since p > 0.05. 

 

9th Student

The findings from the z analysis were to assess whether there was any child who appeared to come from a SDP that differed with the one used in the null hypothesis. Results from z analysis show that the p-value is 0.147 at z < 1.05. As such, we accept the null hypothesis since p > 0.05. 

10th Student

The findings from the z analysis were to assess whether there was any child who appeared to come from a SDP that differed with the one used in the null hypothesis. Results from z analysis show that the p-value is 0.115 at z < 1.20. As such, we accept the null hypothesis since p > 0.05. 

 

 

References

Azzalini, A. (2017). Statistical inference based on the likelihood. Routledge.

Silvey, S. D. (2017). Statistical inference. Routledge.