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Demonstrates I can reproduce the following computer output of the report using the sample allocated to me on moodle. Details of exactly how the computer does simple calculations is provided

1. Summary of the variable ‘does the customer want a unisex gym’ just considering the females
2. Summary that lets you investigate the relationship between the variable ‘time on cardio machine’ and the variable ‘time on weight machine’
3. Summary that lets you investigate the relationship between the variable ‘does the customer want a unisex gym’ and ‘gender’
4. Summary that lets you investigate the relationship between the variable ‘time spent on the cardio machine’ and ‘gender’

Demonstrates I can calculate the following using my own sample
a) The confidence interval for the proportion of females that want a unisex gym

1. b) The confidence interval for the proportion of males that want a unisex gym
2. c) The test stat for testing the claim the majority of females want a unisex gym, this is the zscore of sample proportion assuming the population proportion is 0.5
3. d) The test stat for testing the claim the majority of males want a unisex gym, this is the zscore of sample proportion assuming the population proportion is 0.5

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

There are two reasons for this
a) I can explain why the different main findings in the report use different methods to summarize data.

1. b) I can find article that discusses gyms and give an appropriate numerical summary using the dataset and state if the article agrees or disagrees with the summary.

Demonstrates I can use a webpage that does all the calculations required for a hypothesis test because I do this using my allocated sample. Appropriate simple conclusions based on the computer output of hypothesis testsDemonstrates I can explain the structure of a good report that uses statisticsDemonstrates I can roughly explain the hypothesis tests used in the sample report including why you think concept of H0 and H1 is or is not useful“

## Calculating Confidence Interval for Proportion of Females that Prefer Unisex Gyms

The scatter plot represent negative slope which indicates that higher spending on cardio by male/female would decrease the time spent on the weight machine. This is because the total time of exercise is usually fixed and it is divided between weight training and cardio. Therefore, if a higher time is spent on cardio, then lower time is spent on weight machine and vice versa (Flick, 2015).

• Pivot table to represent the customers that want or do not want unisex gym is highlighted below.

It can be said based on the above that 64.86% of female prefer unisex gym while 35.14% male prefer unisex gym. Further,  64.86% - 35.14 % = 29.72% more female would prefer to go unisex gym.

• Pivot table to represent the relationship between the time spent on cardio machine with the gender of customer.
• Females are spending a mean of 36.48 minutes ion cardio while males are spending only 15 minutes on cardio. Hence, females would spend 36.48 minutes – 15 minutes = 21.48 minutes more on an average on cardio machine.

• 90% confidence interval for the sample proportion of female who will say yes to Unisex gym
• 90% confidence interval for the sample proportion of male who will say yes to Unisex gym

For female customers

Total female customers in sample

Number of female who would prefer unisex gym = 24

Sample proportion of female who would prefer unisex gym

Standard error of sample proportion

The z value of 90% confidence interval = 1.645

Lower limit 90% confidence

Upper limit 90% confidence

Thus, 90% confidence interval would be [0.4220   0.6689

For male customers

Total male customers in sample

Number of male who would prefer unisex gym = 13

Sample proportion of male who would prefer unisex gym

Standard error of sample proportion

The z value of 90% confidence interval = 1.645

Lower limit 90% confidence

Upper limit 90% confidence

Thus, 90% confidence interval would be [0.1393   0.3249]

• Test statistics needs to be determined if the case when number of females going to the unisex gym is higher than 50%.

Total female customers in sample

Number of female who would prefer unisex gym = 24

Sample proportion of male who would prefer unisex gym

Number of females going to the unisex gym

The p value for the z stat

Assume level of significance = 5%

It can be said that p value is higher than level of significance and hence, null hypothesis would not be rejected. Therefore, it can be concluded that proportion of female prefer unisex gym is not higher than 50% (Hair et. al., 2015).

• Test statistics needs to be determined if the case when number of males going to the unisex gym is higher than 50%

Total male customers in sample

Number of male who would prefer unisex gym

Sample proportion of male who would prefer unisex gym

Number of males going to the unisex gym

The p value for the z stat is 1

Assume level of significance = 5%

It can be said that p value is higher than level of significance and hence, null hypothesis would not be rejected. Therefore, it can be concluded that proportion of male prefer unisex gym is not higher than 50% (Hillier, 2016).

(a) With regards to data summary, it is essential to note that the techniques used would suitably vary. For instance, if the relationship between two variables needs to be summarised when atleast one of them is categorical, then the same would be achieved through cross tabulation table which was apparent when the preferences of male and female were summarised. However, when both the given variables are numerical in nature, then the summary of the relationship can be better represented through the use of scatter plot which is quite informative. This has been exhibited in this report when summary of the relationship between weight machine time and cardio time had to be presented. As a result, the suitable mechanism for summary tends to vary in accordance with the underlying data type (Eriksson and Kovalainen, 2015).

## Appropriate Methods for Summarizing Different Types of Data

(b) The given article tends to highlight the significant differences in preferences when it comes to males and female gym members. Males tend to have a specific agenda and prefer to choose athletic activities which do not require much dance or coordination. The social aspect at gyms is not very significant as it is a competitive activity for them. In contrast, females tend to focus less on weight training and more on aerobics and yoga which require coordination. Also, the associated social aspects for them are very critical. Further, the article also highlights how the preferences of the two genders tend to be driven by two factors namely their physical attributes and social norms (Sorgen, nd).

The above difference is captured in the cross tabulation summary of reason to go to gym

H0 :p1= p2  i.e. the proportion of female members who prefer unisex gym and the proportion of male members who prefer unisex gym does not exhibit any significant difference.

HA :p1≠ p2 i.e. the proportion of female members who prefer unisex gym and the proportion of male members who prefer unisex gym does exhibit significant difference.

The p value comes out to be 0.00. Since the p value has come out to be lower than the significance level of 0.05, hence the null hypothesis would be rejected while the alternative hypothesis would be accepted (Flick, 2015).

• Hypothesis testing

H0 :µ1= µ2  i.e. the mean time spent by female members on cardio does not significantly differ from the mean time spent by male members on cardio.

HA :µ1≠ µ2 i.e. the mean time spent by female members on cardio does significantly differ from the mean time spent by male members on cardio. The p value comes out to be 0.00. Since the p value has come out to be lower than the significance level of 0.05, hence the null hypothesis would be rejected while the alternative hypothesis would be accepted (Hair et. al., 2015).

Based on the hypothesis testing conducted in the previous section, it may be concluded that there is a higher preference of unisex gym from females as compared to males. This is not surprising considering that females tend to be usually more comfortable in unisex gyms. Additionally, it can also be also be concluded that the mean times spent on cardio by both sexes tend to differ. This is also not surprising since the males typically tend to devote more time towards weight machines unlike females who are more inclined to cardio. This arises owing to the different expectations from a male and female with regards to key physical attributes.

The given report has a logical structure which is apparent from the flow that is visible across the various sections. In section 1, the focus is on highlighting the summary of the provided sample data while in section 2, the focus is on deriving estimates about the population with regards to the preferences of the two sexes. In section 3, a particular article regarding the given research has been chosen and suitable summary is present of the attached data.

Further, in section 4, hypothesis testing has been used to draw conclusion about key research questions which is presented in section 5. The only aspect which seems missing is the lack of an introduction which would have provided a background context to the reader and would have therefore enhanced the overall utility in this case.

The hypothesis tests are not very easy to understand owing to the underlying statistical nature of these tests where a host of computations may be involved. However, with practice, these tests tend to become quite understandable especially if one can understand the basic steps of hypothesis testing. These include defining the hypothesis, level of significance, conducting the test, analysing the result and reaching the conclusion (Eriksson and Kovalainen, 2015).

The use of computers is highly recommended for conducting hypothesis tests as the datasets are usually quite large and the statistical computations of these datasets can be cumbersome for the user besides being prone to human errors. In this light, it is advisable that the hypothesis test must be performed with the help of computer and similar technology aids. However,

it is noteworthy that even while using computer, it is essential that the user must have awareness about the various tests so that suitable test can be chosen which requires thorough understanding of the underlying assumptions with regards to data distribution.  Thus, it may be concluded that computers should be used only as a calculation aid and not a substitute for understanding of this vital statistical tool (Hillier, 2016).

References

Eriksson, P. and Kovalainen, A. (2015) Quantitative methods in business research 3rd ed. London: Sage Publications.

Flick, U. (2015) Introducing research methodology: A beginner's guide to doing a research project. 4th ed. New York: Sage Publications.

Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., and Page, M. J. (2015) Essentials of business research methods. 2nd ed. New York: Routledge.

Hillier, F. (2016) Introduction to Operations Research 6th ed. New York: McGraw Hill Publications.

Sorgen, C. (n.d.) When it comes to working out, men and women are from different planets, [Online] Available at https://www.webmd.com/fitness-exercise/features/his-hers-fitness#1 [Assessed September 16, 2018].

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