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Owner: kmm17k
Created: Dec 14, 2017
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Responses to Soda Part 4
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Data set 1. Responses to Soda survey   [Info]
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Sample or Population:

My dataset is a sample of 349 individuals, it is not a population because it does not take into acount the entire population rather that it takes a sample of some of the individuals in the population.

Result 1: One sample T hypothesis test (Soda)   [Info]
One sample T hypothesis test:
μ : Mean of variable
H0 : μ = 18
HA : μ ≠ 18

Hypothesis test results:
VariableSample MeanStd. Err.DFT-StatP-value
Soda18.8958211.49616123340.598746250.5497

T-Test:

The variable used in the test was soda intake (%). The null hypothesis (Ho) was sample mean=18, while the alternative hypothesis (Ha) was the sample mean ≠ 18.

After performing a T-test because my dataset is a sample, the T-stat is 0.59874625. The P-value is 0.5497. Since the P-value is larger than the significance level (0.05) we fail to reject the null hypothesis.


Result 2: Contingency table Gender/Soda (with data)   [Info]
Contingency table results:
Rows: Gender
Columns: Soda
0 to 2020 to 4040 to 6060 to 8080 to 100100 to 120Total
Female113132111110169
Male11522510101163
Total228352621211332

Chi-Square test:
StatisticDFValueP-value
Chi-square513.1690890.0218

Contingency Table:

The variables included in the contingency tables are gender and soda intake (%). While the null hypothesis states that there is no relationship between gender and soda intake, the alternative hypothesis states that the two factors are dependant and maintain a relationship.

The statistic, Chi-Squared, came out to 13.169089. The P-value is 0.0218. Since the P-value is less than the significance level (0.05), we can conclude to reject the null hypothesis. Therefore, it can be concluded that there is a relationship between soda intake (%) and gender.


Result 3: One Way ANOVA (Soda and Age)   [Info]
Analysis of Variance results:
Data stored in separate columns.

Column statistics
ColumnnMeanStd. Dev.Std. Error
Soda33518.89582127.3842461.4961612
Age33630.34806513.6662560.74555539

ANOVA table
SourceDFSSMSF-StatP-value
Columns122001.01922001.01947.019679<0.0001
Error669313032.37467.91087
Total670335033.39

One Way ANOVA:

The variables included in the One Way ANOVA are age and total soda intake (%). The null hypothesis is that the sample mean of age and soda intake are equal while the alternative hypothesis is that the samples means of both age and soda intake are different.

Using the ANOVA statistic test, it was found that the F-stat was 47.019679. The P-value is less than 0.0001, and since this is less than the significance level (.05), the null hypothesis will be rejected, indicating that the sample means are different.


 

Result 4: Extra Credit #1: One sample Z hypothesis test (Soda)   [Info]
One sample Z hypothesis test:
μ : Mean of variable
H0 : μ = 18
HA : μ ≠ 18
Standard deviation not specified.

Hypothesis test results:
VariablenSample MeanStd. Err.Z-StatP-value
Soda33518.8958211.49616120.598746250.5493

Extra Credit #1:

The variable used in the test was soda intake (%). The null hypothesis (Ho) was sample mean=18, while the alternative hypothesis (Ha) was the sample mean ≠ 18.

After performing a Z-test, my data was extremely similar when compared to the T-test calculated with the same variable. While my t-stat remained at 0.59874625, my P-value slightly changed from 0.5497 for the T-test  and 0.5493 for my Z-test.

Although numerically different, the P-value is still greater than the significance level (0.05), and therefore we fail to reject the null hypothesis .


Result 5: Extra Credit #2 Contingency table Age/Diet (with data)   [Info]
Contingency table results:
Rows: Diet
Columns: Age
0 to 2020 to 4040 to 6060 to 8080 to 100Total
No53891941166
Yes1342373095
Total661315671261

Chi-Square test:
StatisticDFValueP-value
Chi-square431.014509<0.0001
Warning: over 20% of cells have an expected count less than 5.
Chi-Square suspect.

Extra Credit #2:

The variables included in the contingency tables are age and diet. While the null hypothesis states that there is no relationship between age and diet, the alternative hypothesis states that the two factors are dependant and maintain a relationship.

The statistic, chi-squared, came out to 31.014509, in which the P-value is less than .0001. Since the P-value is less than the significance level (.05), you can conclude to reject the null hypothesis. Therefore, it can be concluded that there is a relationship between age and diet.


Result 6: Extra Credit #3: One Way ANOVA (Age/Diet)   [Info]
Analysis of Variance results:
Responses: Age
Factors: Diet

Response statistics by factor
DietnMeanStd. Dev.Std. Error
No16626.65662712.1623930.94398477
Yes9535.56789514.0342911.4398879

ANOVA table
SourceDFSSMSF-StatP-value
Diet14798.11024798.110228.952904<0.0001
Error25942921.792165.72121
Total26047719.902

Extra Credit #3:

(since my data only had 2 quantitative and 2 qualitative variables, I used both my quantitative variables for the first ANOVA test, and will use the response of Age with the factor of Diet)

The variables included in the One Way ANOVA are age and diet. The null hypothesis is that the sample means of age and diet are equal to one another while the alternative hypothesis is that the samples means of both age and diet are different to one another.

Using the ANOVA statistic test, it was found that the F-stat was 28.952904. The P-value was less than .0001, and since this is less than the significance level (0.05), the null hypothesis is rejected, indicating that the sample means are different.

 

Extra Credit #4:

While my dataset contains enough individuals who participated in the sample to accuratley display my data and make accurate conclusions regarding the soda intake and the ages, diet, and gender of those who do or do not intake soda and how much (%) there are more things I would like to be informed about regarding my sample. For example in a few instances under the diet variable, some individuals refused to answer yes or no. I would like to know for what reasons and if them answering yes or no , if it would effect the results and conclusions in any way. I would also like to witness that if more individuals were sampled would the distribution of my data become a more normal distribution, all though I know this to be true on a thoretical scale, I would like to witness it through physical data and graphs regarding my data set.

HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=74594">Responses to Soda Part 4</A>

Comments
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By xg15
Dec 14, 2017

In hypothesis testing, we are testing the population mean. Sample mean is determined once we have the data.

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