Report On Gym Preferences: Data Analysis And Hypothesis Testing

Section 1 reproduction of the data summaries including details of simple calculations

“Section 1 reproduction of the data summaries  including details of simple calculations

1a) Summary of the variable ‘do the customers want a unisex gym’ just considering the females “

gender	Female
Row Labels Save Time On Research and Writing Hire a Pro to Write You a 100% Plagiarism-Free Paper. Get My Paper	Count of Should the gym be Unisex?
no	27
yes	28
Grand Total	55

The sample proportion that say yes is;

The calculation clearly shows that the percentage of the female participants who want a unisex gym is 50.91% (Morey, Hoekstra, Rouder, Lee, & Wagenmakers, 2016).

 “ 1b) Summary of the relationship between the variables ‘time on cardio machine’ and ‘time on weight machine’ “

The above scatter clearly indicates that there is a positive linear relationship between minutes on Cardio and minutes on weight machine.

 “1c) Summary that lets you investigate the relationship between the variable ‘does the customer want a unisex gym’ and ‘gender’ “

Count of Should the gym be Unisex?	Column Labels
Row Labels	no	yes	Grand Total
Female	27	28	55
Male	35	10	45
Grand Total	62	38	100

Count of Should the gym be Unisex?	Column Labels
Row Labels	no	yes	Grand Total
Female	49.09%	50.91%	100.00%
Male	77.78%	22.22%	100.00%
Grand Total	62.00%	38.00%	100.00%

The above tables shows that a large percentage of the female participants would desire to have a unisex gym when compared to the male participants.

“1d)Summary that lets you investigate the relationship between the variable ‘time spent on the cardio machine ’ and ‘gender’ “

Row Labels	Average of Minutes on Cardio	StdDev of Minutes on Cardio
Female	37.364	17.661
Male	17.000	16.563
Grand Total	28.200	19.893

Female participants were on average found to spend more time on Cardio machine as compared to the male participants. As can be seen, females on average spent 37.36 (SD = 17.66) while males on average spent 17.00 (SD = 16.56).

“Section 2: calculation of confidence intervals and test statistics

2a) Calculation of confidence interval for the proportion of females that prefer a Unisex gym using my allocated sample”

90% confidence interval for sample proportion for females

Count of Should the gym be Unisex?	Column Labels
Row Labels	no	yes	Grand Total
Female	27	28	55
Male	35	10	45
Grand Total	62	38	100

Considering females only, we have;

N = 55,

Sample proportion

 Standard error of sample proportion =  

90% confident the true proportion is between

Lower limit:

Upper limit:

 “2b) Calculation of confidence interval for the proportion of males that prefer a Unisex gym using my allocated sample”

Note you use the information from section 1c

90% confidence interval for sample proportion for males

Count of Should the gym be Unisex?	Column Labels
Row Labels	no	yes	Grand Total
Female	27	28	55
Male	35	10	45
Grand Total	62	38	100

Considering males only, we have;

N = 45,

Sample proportion

 Standard error of sample proportion =  

90% confident the true proportion is between

Lower limit:

Upper limit:

“2c) Calculation of Test stat for checking if the females that want a unisex gym is above 50% (Find the sample proportion’s zscore assuming p=0.5) using my allocated sample”
Test stat    assume p=0.5

Count of Should the gym be Unisex?	Column Labels
Row Labels	no	yes	Grand Total
Female	27	28	55
Male	35	10	45
Grand Total	62	38	100

Considering females only, we have;

N = 55,

Sample proportion

 =

The computed z-score is much less as compared to the critical z value of 1.96; this means that the null hypothesis is not rejected and by not rejecting the null hypothesis we conclude that the proportion of females who want a unisex gym is not above 50%.

“2d) Calculation of Test stat for checking if the males that want a unisex gym is above 50% (find the z score of proportion assuming p=0.5) using my allocated sample”

Test stat for checking if the males that want a unisex gym is above 50%

Count of Should the gym be Unisex?	Column Labels
Row Labels	no	yes	Grand Total
Female	27	28	55
Male	35	10	45
Grand Total	62	38	100

Considering males only, we have;

N = 45,

Sample proportion

=

The computed absolute z-score (3.7271) is greater than the critical z value of 1.96; we therefore reject the null hypothesis and conclude that the proportion of males who want a unisex gym is below 50%.

1a) Summary of the variable ‘do the customers want a unisex gym’ just considering the females

“Section 3

Evidence I can decide the appropriate method to summarize data based on the nature of data (the variable types)

1. My explanation why the different main findings in the sample report use different methods to summarize data. “

The study employed different methods to summarize data since the data had different scales and data types. For instance, there are 4 variables; gender, prefer unisex, time on cardio and time on weight machine. Two of the variables; gender and prefer unisex gym were qualitative variables while time on cardio and time on weight machine were quantitative variables (Steiger, 2004).

When it came to analysis, the authors presented frequency tables for the qualitative (nominal) variables while descriptive statistics such as mean and standard deviation were provided for the quantitative variables such as time on cardio and time on weight machine (Kiefer, 1977).

1. “My summary of an article that discusses gyms and an appropriate numerical summary using my allocated sample from the section 3 dataset”

We sought to compare the BMI of the Americans male and females using the provided dataset and one from the online article. The link to the online article is https://www.cdc.gov/nchs/data/nhanes/databriefs/adultweight.pdf

In the article, the authors report the average BMI for the male adults to be 26.6 while that of the female adults to be 26.5. The results from the article is given below;

We tried to verify the information above using the dataset that was provided. Results showed that the average BMI for the female Americans was 25.96 while the average BMI or the male Americans was found to be 26.66.

sample	330
Row Labels	Average of BMI
female	25.96
male	26.66
Grand Total	26.25

 “Section 4 my discussion of the webpages used to do all the calculation of a hypothesis tests

4a use a webpage to do a hypothesis test of the difference between two proportions using my allocated sample  

Using

https://www.socscistatistics.com/tests/ztest/Default2.aspx

The p-value is given as 0.00328 (a value less than 5% level of significance), this results to rejection of the null hypothesis and concluding that the proportion of female participants who wish to have a unisex gym is significantly higher than that of the male participants (Mayo, 1981).

“”“4b) a use a webpage to do a hypothesis test of the difference between two means using my allocated sample

Using

https://www.graphpad.com/quickcalcs/ttest1/?Format=SD

“

 “The output is “

This section sought to test whether there is significant difference in the amount of time spent on cardio machine by the male and the female respondents. Results showed that female respondents take significantly more time on cardio as compare to male respondents.

“Section 5

Appropriate simple conclusions based on the computer output of hypothesis tests in section 4”

For the first part, the p-value was found to be 0.00328 (a value less than 5% level of significance), this resulted to rejection of the null hypothesis and concluding that the proportion of female participants who wish to have a unisex gym is significantly higher than that of the male participants.

For part 2 of section 4, the researcher sought to test whether there is significant difference in the amount of time spent on cardio machine by the male and the female respondents. Results showed that female respondents take significantly more time on cardio as compare to male respondents.

“Section 6
Demonstrates I can explain the structure of a good report that uses statistics “

The study basically sought to understand the stand of the female and male participants in regard to support for a unisex gym. Participants were asked whether the gym should be a unisex gym or not. The study also sought to understand how long the male and the female respondents take on both the cardio machine and the weight machine. To analyse this, several techniques were employed. Some of the techniques used include the one sample t-test for proportions and two-sample proportions test.

In my opinion I can evidently say that the report is well prepared and the structure of the report is great.

“Section 7
Demonstrates I can explain the hypothesis tests used in report and hypothesis testing in general“

Hypothesis test is the test that is used to verify or deny a claim.  There are four different hypothesis that were tested in this study.

The tested hypothesis are derived from the research questions. The first research question is “Is the proportion of female participants who want a unisex gym above 50%?

The hypothesis tested is;

Where  is the proportion of female participants who want a unisex gym.

The second research question is “Is the proportion of male participants who want a unisex gym above 50%?

The hypothesis tested is;

Where  is the proportion of male participants.

The third research question is “Is the proportion of female participants who want unisex gym same as the proportion of male participants?”

The hypothesis associated with it is; 

Where  is the proportion for the female participants who want unisex gym while  is the proportion for the male participants who want unisex gym.

The forth and the last research question is “Is there significant difference in the mean time spent on cardio for the male and female participants?”

Where  is the mean time taken in the cardio by the female participants while  is the mean time taken in the cardio by the male participants.

References

Kiefer, J. (1977). Conditional Confidence Statements and Confidence Estimators (with discussion). Journal of the American Statistical Association, 72 (360a), 789–827. doi:10.1080/01621459.1977.10479956

Mayo, D. G. (1981). In defence of the Neyman-Pearson theory of confidence intervals. Philosophy of Science, 48(2), 269–280.

Morey, R. D., Hoekstra, R., Rouder, J. N., Lee, M., & Wagenmakers, E. (2016). The Fallacy of Placing Confidence in Confidence Intervals. Psychonomic Bulletin & Review, 23(1), 103–123. doi:10.3758/s13423-015-0947-8

Steiger, J. H. (2004). Beyond the F test: Effect size confidence intervals and tests of close fit in the analysis of variance and contrast analysis”. Psychological Methods. American Psychological Association, 9(2), 164–182. doi:10.1037/1082-989x.9.2.164