Question:
Due to financial hardship, the Nyke shoe company feels they only need to make one size of shoes, regardless of gender or height. They have collected data on gender, shoe size, and height and have asked you to tell them if they can change their business model to include only one size of shoes – regardless of height or gender of the wearer. In no more 5-10 pages (including figures), explain your recommendations, using statistical evidence to support your findings. The data found are below:
Shoe Size | Height | Gender | 5.00 | 63.00 | Female | 7.50 | 70.00 | Female | 9.00 | 70.00 | Female | 7.00 | 64.00 | Male | 11.00 | 72.00 | Male | 12.00 | 72.00 | Male | 14.00 | 76.00 | Male | 7.00 | 66.00 | Female | 7.50
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We can also test if there is a significant difference between the average height for females and the average height for the males.
Denote by the average heights for males and females, respectively. Here are the two hypotheses:
Null hypothesis H0:
Alternative hypothesis Ha:
We conduct an independent sample t-test using Excel, and obtain the following output (see t-test-height)
t-Test: Two-Sample Assuming Unequal Variances | | | | | height (F) | height(M) | Mean | 66.66666667 | 71.35294118 | Variance | 11.88235294 | 9.867647059 | Observations | 18 | 17 | Hypothesized Mean Difference | 0 | | df | 33 | | t Stat | -4.207413941 | | P(T<=t) one-tail | 9.30285E-05 | | t Critical one-tail | 1.692360258 | | P(T<=t) two-tail | 0.000186057 | | t Critical two-tail | 2.034515287 | |
From the above output, we can see that the p-value is 0.000186, which is smaller than 0.05 (if we select a 0.05 significance level).
So, we should reject the null hypothesis H0. At a 0.05 level of significance level, we conclude that there is a significant difference between the average height for females and the average height for the males.
Conclusion:
According to above analysis, we have found that there is a strong positive correlation between the shoe sizes and heights.
We also found
Because the p-value of .035 is less than the significance level of .05, I will reject the null hypothesis at 5% level.
When you perform a test of hypothesis, you must always use the 4-step approach: i. S1:the “Null” and “Alternate” hypotheses, ii. S2: calculate value of the test statistic, iii. S3: the level of significance and the critical value of the statistic, iv. S4: your decision rule and the conclusion reached in not rejecting or rejecting the null hypothesis. When asked to calculate p–value, S5, relate the p-value to the level of significance in reaching your conclusion.
t = −3.15 describes the difference between women and men for what variable in this study? Is this value significant? Provide a rationale for your answer.
c) What is the null and alternative hypothesis? Do the data results lead you to reject or fail to reject the null hypothesis?
With a P-value of 0.00, we have a strong level of significance. No additional information is needed to ensure that the data given is accurate.
Due to financial hardship, the Nyke shoe company feels they only need to make one size of shoes, regardless of gender or height. They have collected data on gender, shoe size, and height and have asked you to tell them if they can change their business model to include only one size of shoes – regardless of height or gender of the wearer. In no more 5-10 pages (including figures), explain your recommendations, using statistical evidence to support your findings. The data found are below:
A pharmaceutical company is testing the effectiveness of a new drug for lowering cholesterol. As part of this trial, they wish to determine whether there is a difference between the effectiveness for women and for men. Using = .05, what is the value the test statistic?
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| Based on explicit knowledge and this can be easy and fast to capture and analyse.Results can be generalised to larger populationsCan be repeated – therefore good test re-test reliability and validityStatistical analyses and interpretation are
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