Assuming you are a product manager of a game website, one of the objectives is to develop games that are quick and doesn$$t require a lot of resources. Now the designing team just came out a couple of puzzle games, and you would like to know on average how long it takes for a person to complete the puzzle game.

We collected players completion time along with some characteristics, the data are stored in the Excel file, where the variables of interest are defined as:

Variable Values

Hand Dominance left handed or right handed

Height Real height in inches $(1$ feet $=12$ inches$)$

Type of Puzzle Cat Puzzle or Giraffe Puzzle

Completion Time time in seconds spent in completing the puzzle

Enjoy Level From one start to $10$ starts, how much the player enjoyed the puzzle game

Is there evidence that the average Enjoy Level of Giraffe Puzzle is significantly higher than Cat Puzzle?

hand dominance Height $($in inches$)$ Type of Puzzle Completion Time $($in seconds$)$ Enjoy Level

right handed $75$ Giraffe $5410$

right handed $70$ Cat $503$

right handed $73$ Cat $2210$

right handed $64$ Giraffe $6810$

left handed $69$ Cat $368$

right handed $72$ Giraffe $875$

right handed $67$ Giraffe $5510$

right handed $68$ Cat $468$

right handed $68$ Cat $561$

right handed $69\mathrm{.}6$ Giraffe $479$

right handed $62$ Giraffe $3310$

right handed $70$ Giraffe $4010$

left handed $75$ Giraffe $4410$

right handed $69$ Giraffe $311$

right handed $71$ Giraffe $8410$

right handed $70$ Giraffe $1107$

right handed $69$ Giraffe $389$

left handed $72$ Cat $787$

right handed $69\mathrm{.}6$ Cat $10010$

right handed $65$ Cat $688$

right handed $71$ Giraffe $605$

right handed $60$ Cat $6510$

right handed $70$ Giraffe $7710$

right handed $74$ Giraffe $4210$

right handed $72$ Giraffe $727$

right handed $72$ Cat $717$

right handed $69$ Cat $5110$

right handed $66$ Giraffe $2710$

right handed $68$ Cat $1028$

right handed $73$ Giraffe $711$

right handed $66$ Cat $5610$

right handed $72$ Cat $646$

right handed $72$ Giraffe $11110$

right handed $66$ Cat $3810$

right handed $71$ Cat $1028$

right handed $70$ Giraffe $4810$

right handed $73$ Giraffe $796$

right handed $70$ Giraffe $476$

right handed $72$ Giraffe $474$

right handed $70$ Cat $607$

right handed $5\mathrm{.}1$ Giraffe $845$

right handed $6$ft Giraffe $7010$

right handed $71$ Cat $447$

right handed $73$ Giraffe $627$

right handed $72$ Giraffe $427$

right handed $67$ Giraffe $507$

right handed $70$ Giraffe $368$

right handed $72\mathrm{.}5$ Giraffe $758$

right handed $71$ Giraffe $885$

right handed $69$ Cat $503$

$1$: Referring to the scenario, what is the relevant hypotheses statement to be tested?

H$0$:$\_\_\_\_\_$Ug $$ Uc $<=0\_\_\_\_\_\_\_$

H$1$:$\_\_\_\_$Ug $$ Uc $>0\_\_\_\_\_\_\_\_$

$2$: Please use data in the excel and conduct the appropriate test$($s$)$ in response to the question in Q$1$ and include the correct output table$($s$)$ from Data Analysis Add$-$in function in excel file as response.

To answer this question, you will need to sort the data based on the type of puzzle first, then conduct the Enjoyment Level between two different puzzles. Please specify which test$($s$)$ you conducted $($t$-$test for paired sample, F test for variance, t$-$test for mean assuming equal variances, t$-$test for mean assuming unequal variances, or two sample proportion Z test$)$ and why.

$3$: The test statistic associate with Q$1$ is $\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ and the p$-$value is $\_\_\_\_\_\_\_\_\_\_\_\_$

$4$: Which of the following represents the correct conclusion?

a$)$ Reject the null and conclude there is enough evidence that the Enjoy Level of Giraffe Puzzle is significantly higher than Cat Puzzle at $\mathrm{.}05$ level.

b$)$ Reject the null and conclude there is enough evidence that the Enjoy Level of Giraffe Puzzle is significantly higher than Cat Puzzle at $\mathrm{.}01$ level.

c$)$ Both a and b are correct.

d$)$ None of the above is correct.

$5$: Which of the following statements reveals a Type I error?

a$.$ Conclude that the Enjoy Level of Giraffe Puzzle is significantly higher than Cat Puzzle when in reality it is not significantly higher.

b$.$ Conclude that the Enjoy Level of Giraffe Puzzle is significantly higher than Cat Puzzle when in reality it is significantly higher.

c$.$ Conclude that the Enjoy Level of Giraffe Puzzle is not significantly higher than Cat Puzzle when in reality it is not significantly higher.

d$.$ Conclude that the Enjoy Level of Giraffe Puzzle is not significantly higher than Cat Puzzle when in reality it is significantly higher.

$6$: Assume that your statistical test indicated that the Enjoy Level of Giraffe Puzzle is significantly higher than Cat Puzzle. Discuss the three conditions of causalities in this case, how confident can we be to conclude it was the design of the of puzzle that caused this difference in Enjoy Level? Describe any confounding variables.

$7.$ Redesign the study to produce a better test of the causal effects of the type of puzzle on the Enjoy Level.