111 112 Two sample dependent and independent samples t-tests for a difference of means quiz

	Momentum before	Momentum after
	173	154
	203	191
	209	210
	213	206
	214	156
	224	192
	224	188
	228	179
	259	271.6
  1. Students in SC 130 Physical Science were seeking to determine whether momentum is conserved in a collision between marbles. The theory is that the momentum before is equal to the momentum after the collision. Each row is a pair of momentum values before and after a collision. What level of measurement is this data?
  2. Calculate the sample mean momentum before.
  3. Calculate the sample mean momentum after.
  4. Based on a t-test for a difference of sample means, calculate the p-value for the paired, two sample data.
  5. At a risk of a type I error (alpha α) of 0.05, do you reject a null hypothesis of no difference in the sample means or fail to reject a null hypothesis of no difference in the sample means?
  6. At an alpha of 5%, based on the data above, was momentum conserved?
  7. For the momentum data, calculate the pooled standard deviation.
  8. For the momentum data, calcuate Cohen's effect size d. Report the value as a positive value, rounded to two decimal places.
  9. Based on Cohen's effect size d, what is the "importance" of the difference: small, medium, or large?

Over the past three years an asymmetry has developed in the FiboBelly ratio data. If the FiboBelly ratio varies in a purely random manner, then the data should distribute normally around the population mean. The distribution, however, is slightly skewed and appears to have a second peak near a ratio of 1.6 One possibility is that there is a gender difference in FiboBelly ratios. For the first time FiboBelly ratios were separated by gender this term. The following questions explore the possibility of a gender difference in the FiboBelly ratios. 

	Male FiboBelly Ratio	Female FiboBelly Ratio
	1.45	1.613
	1.59	1.448
	1.43	1.369
	1.36	1.467
	1.42	1.292
	1.44	1.419
	1.4	1.319
	1.27	1.6
	1.38	1.38
	1.52	1.47
	1.53	1.46
	1.606	1.45
	1.46	1.45
	1.38	1.45
	1.45	
	1.44	
	1.46	
	1.438	
	1.45
  1. Calculate the mean male FiboBelly ratio.
  2. Calculate the mean female FiboBelly ratio.
  3. Based on a t-test for a difference of sample means, calculate the p-value for the independent two sample data.
  4. At a risk of a type I error (alpha α) of 0.05, do you reject a null hypothesis of no difference in the sample means or fail to reject a null hypothesis of no difference in the sample means?
  5. At an alpha of 5%, based on the data above, is the mean FiboBelly ratio different for males and females?