Comparing Statistical Techniques

Comparing Statistical Techniques
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Comparing statistical techniques
Chapter nine
Problem 1
The null hypothesis in the research is usually deemed to be true while the alternative hypothesis (experimental hypothesis) can be used to discredit the null hypothesis (Lutemann, 2008).
Null hypothesis for the research is
H0: The fraction of the American population that has seen a UFO is one person for every one thousand people.
Alternative hypothesis is
Ha: The proportion of the American population that has seen a UFO is less than one person for every one thousand people.
Problem 2
H0: t≥18.4Ha: t<18.4H0: The average time spent by the tenth graders each week watching television stays to be greater or equal to 18.4 hours.
Ha: The average time spent by the tenth graders each week watching television is less than 18.4 hours.
Problem 3
The P-value obtained from the data must be less than 0.05 for the null hypothesis to be rejected (Bennett, Briggs, & Triola, 2014). Conversely, the null hypothesis is accepted in a situation where the P-value is more than 0.05 or when it is equal to 0.05. In this case, the P-value will be
p=0.052=0.025<0.05Problem 4
Given a significance level of 5%, the P-value for each of the tails will be calculated as
p=0.052=0.025Therefore, the right tail will have a P-value of 0.025. The required percentile for rejecting the null hypothesis is given as
1-0.025=0.975 or 97.5%Problem 5
Type I error is a situation where the researcher rejects the null hypothesis even though the null hypothesis is true.

It means that the researcher accepts the alternative hypothesis when the results can be attributed to chance. Likewise, Type II error occurs in case the null hypothesis is not rejected despite the results of the null hypothesis not being true (Bennett, Briggs, & Triola, 2014).
An example is when a researcher wants to compare how effective two different medications are. The researcher may define the null hypothesis by connecting the two medications to have the same level of effectiveness while the alternative hypothesis may state that the two are not equally effective. Type I error happens if the researcher makes a conclusion that the two medications are different while in reality, they are not. Type II error will occur if the researcher acknowledges that the two medications are the same while they have different effects on the patient.
Chapter 10
Problem 1
From the Excel file,
Sample size is n=20
Sample mean = 8.75
Sample standard deviation = 4.733697787

(Data attached in excel file)

Since the critical values are ±2.093, the rejection region is at t<-2.293 or t>2.093.
T-test score = 2.59804796
Mean = 8.75.
The point at which the test is significant is at a P-value of 0.017659.
HO: θ=6
HO: θ≠6 Respectively.
Since t>2.093, the null hypothesis is not accepted.
Problem 2
Output data
Independent Samples Test
Levene’s Test for Equality of Variances t-test for Equality of Means
F Sig. t df
Time Equal variances assumed 4.789 .042 -3.275 18
Equal variances not assumed -3.275 13.509
The P-value is equal to 0.0042, and the Static F-value is equal to -3.275
Group Statistics
Normal_Overweight N Mean Std. Deviation Std. Error Mean
Time 1.00 10 589.0000 42.61455 13.47590
2.00 10 684.9000 82.22523 26.00190
Independent Samples Test
t-test for Equality of Means
Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference
Lower
Time Equal variances assumed .004 -95.90000 29.28650 -157.42865
Equal variances not assumed .006 -95.90000 29.28650 -158.92794
Difference in Group 1 and Group 2
First group

Second group

Group 1 2 Difference
Mean 589 684.9 95.9
SD 42.61 82.23 39.62

The null and the alternative hypothesis
HO: No difference exists in the time spent to take a meal at McDonald’s for overweight individuals compared to normal weight people.
Ha: A significant difference exists in the time spent taking a meal at McDonald’s for overweight individuals compared to normal weight individuals.
The results show that there is a statistically significant difference in the time taken by normal weight individuals to finish a meal compared to overweight people.
Problem 3
(Data attached in Excel file)

The percentage is calculated as 940=0.225 or 22.5%The proportion is given as
2020*100=100%Chi-square test
Parent
1.00 2.00
Count Count
Math .00 20 11
1.00 0 9
Pearson Chi-Square Tests
Parent
Math Chi-square 11.613
df 1
Sig. .001*,b
From the Chi-square test results, the p-value equals 0.001 and d.f =1. Since p≤0.001, the results are significant. It means that the females who are raised by both parents have a higher likelihood of taking up advanced math.
Null and alternative hypothesis
HO: The family structure does not determine whether a female student takes advanced math class.
Ha: The family structure determines whether a female student takes advanced math class.
From the results, the null hypothesis is rejected since there is a significant difference (Lutemann, 2008), in this case, p≤0.001, between the groups.
Problem 4
Data attached in the Excel file.

From the data,
F-score = 7.
P-value = 0.027
Since 0.027<0.5, the results of the analysis are significant.
Post hoc Analysis (Data in file)
Multiple Comparisons
Dependent Variable: Scores
Tukey HSD
(I) Group (J) Group Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
1.00 2.00 -1.00000 .81650 .483 -3.5052 1.5052
3.00 -3.00000* .81650 .024 -5.5052 -.4948
2.00 1.00 1.00000 .81650 .483 -1.5052 3.5052
3.00 -2.00000 .81650 .109 -4.5052 .5052
3.00 1.00 3.00000* .81650 .024 .4948 5.5052
2.00 2.00000 .81650 .109 -.5052 4.5052
Scores
Tukey HSDa
Group N Subset for alpha = 0.05
1 2
1.00 3 2.0000 2.00 3 3.0000 3.0000
3.00 3 5.0000
Sig. .483 .109
From the Post hoc Analysis data, the results are significant between group 1 and group 3 since 0.024 is less than 0.05 (analysis done at a confidence interval of 0.05).
The results from the analysis indicate that the first and the second group are not significantly different. Also, the second and the third group are not significant. However, group one and group three have the strongest difference.

References
Bennett, J. O., Briggs, W. L., & Triola, M. F. (2014). Statistical reasoning for everyday life. Boston: Pearson Education.
Picciano A.G. (2007, November 23).Chi Square. Retrieved from http://www.youtube.com/watch?v=xbFfFws0L1c&feature=PlayList&p=B54BD5982525DA16&index=29
Lutemann. (2008, July 1). Hypothesis Testing, Part 1 of 2. Retrieved from http://www.youtube.com/watch?v=rHAxhlmbRPU&feature=PlayList&p=B54BD5982525DA16&playnext=1&playnext_from=PL&index=13