- It’s hard to tell because the range of the box plots is the same, but perhaps there is a difference because the median for women is 2 and the median for men is 1.
Name of Test:T-test
Conditions and Assumptions: Stated that the sample was random. Sample size is 654, which is large enough (greater than 40).
Hypotheses:
The mean number of friends that adult American men have is two.
The mean number of friends that adult American men have is not two.
Formula:
Calculations:= -2.002299751; p-value = 0.0456655379
Degrees of freedom = 653
Sketch:
Conclusion: Based upon the p-value of 0.0456655379, there is sufficient evidence to reject the null hypothesis that the true population mean of friends for adult American men is 2 at the = 0.05 level. If the null hypothesis were true, the probability of getting a of 1.86608563 or more extreme is 0.0456655379.
Name:T-interval
Conditions and Assumptions: Stated that the sample was random. Sample size is 813, which is large enough (greater than 40).
Formula:
Calculations: = 1.9674 to 2.2091
Degrees of freedom = 812
Conclusion: We are 95% confident that the true population mean of friends for adult American women is between 1.9674 and 2.2091. If we constructed 100 confidence intervals of size 813, we would expect 95 of them to capture the true population mean.
Name of Test: 2 Sample T-test
Conditions and Assumptions: Stated that the samples were random. Samples are independent of each other. Sample sizes are 654 and 813 both of which are large enough (greater than 40).
Hypotheses:
The mean number of friends adult American women is equal to the mean number of friends adult American men have.
The mean number of friends adult American women is greater than the mean number of friends adult American men have.
Formula:
Calculations: = 2.449742587; p-value = 0.007209124
Degrees of freedom = 1392.751285
Sketch:
Conclusion: Based upon the p-value of 0.007209124, there is sufficient evidence to reject the null hypothesis that the true population mean of friends for adult American women is equal to the true population mean of friends for adult American men at the = 0.01 level. If the null hypothesis were true, the probability of getting a test statistic of 2.4497 or more extreme is 0.007209124.
Name: 2 Sample T-interval
Conditions and Assumptions: Stated that the samples were random. Samples are independent of each other. Sample sizes are 654 and 813 both of which are large enough (greater than 40).
Formula:
Calculations: = 0.04537 to 0.41004
Degrees of freedom = 1392.75
Conclusion: We are 95% confident that adult American females have between 0.04537 to 0.41004 more friends than adult American males. If we constructed 100 confidence intervals of size 1467, we would expect 95 of them to capture the true difference in population means.
- Not really because the results indicate that the largest the difference might be is 0.4 of a friends or it may be as small as almost zero.
Name of Test: 2 Sample T-test
Conditions and Assumptions: Stated that treatments are randomly assigned. The two groups are independent of each other. Looking at the box plots (you should make these on your calculator, too), it appears ok to assume that they can from a normal population, except the crossfit data is pretty skewed.
Hypotheses:
The mean amount of bench press gain for the hammer strength program is equal to the mean amount of bench press gain for the crossfit program.
The mean amount of bench press gain for the hammer strength program is not equal to the mean amount of bench press gain for the crossfit program.
Formula:
Calculations: = -0.7098852075; p-value = 0.4958214412
Degrees of freedom = 8.966173361
Sketch:
Conclusion: Based upon the p-value of 0.4958214412, there is not sufficient evidence to reject the null hypothesis that the true mean gain in bench press for hammer strength is equal to the true mean gain in bench press for crossfit at any reasonable significance level. If the null hypothesis were true, the probability of getting a test statistic of –0.70988 or more extreme is 0.4958214412.
Name of Test: 2 Sample T-interval
Conditions and Assumptions: Stated that treatments are randomly assigned. The two groups are independent of each other. Looking at the box plots, it appears ok to assume that they can from a normal population, except the crossfit data is pretty skewed.
Formula:
Calculations: = -11.38 to 5.0266
Degrees of freedom = 8.966173361
Conclusion: We are 90% confident that the mean difference in bench press gain is between –11.38 to 5.0266 – meaning that crossfit may be 11.38 pound higher or hammer strength may be 5.03 pounds higher. If we constructed 100 confidence intervals of size 16, we would expect 90 of them to capture the true difference in population means.
- No, because the confidence interval includes 0.
- 18.99999999999999999999999999999% (0.50 – ½ 0.81) X 2