theme park owner wants to know if the children’s rides are favoring 10 year old girls...

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theme park owner wants to know if the children’s rides arefavoring 10 year old girls over 10 year old boys based on height.In other words, does one group taller than the other and thus cango on more rides?
Part a: The ownergathered height data on 10 year old girls and 10 year old boys, seedata below. Determine at the 5% significance level if there isevidence that the two genders are not the same height and thuscannot all go on the same rides. Show your work and give youranswer in complete sentences in context of the problem.
10 year old girls 10 year old boys
52.3 58.1
53.5 53.0
53.6 56.2
53.0 54.2
56.9 50.9
51.2 54.4
48.6 51.4
51.3 53.5
53.9 51.0
54.0 59.7
57.5 53.4
53.7 49.2
55.7 55.7
54.9 55.1
57.9 57.7
56.9 57.7
59.9 52.6
56.6 54.7
54.6
52.9
52.0
56.0
Part b: After doingsome research, the owner found the following information about theexpected height and standard deviation for 10 year olds. Does thatchange the result of part a? Show your work andgive your answer in complete sentences in context of theproblem.
10 year old girls
10 year old boys
Average height
54.5 inches
54.5 inches
St. deviation
2.74 inches
2.71 inches

Answer & Explanation Solved by verified expert

3.6 Ratings (283 Votes)

Part a Solution Two sample t test for population means assuming pooled variance Null hypothesis H0 The mean height of 10 year old girls is same as the mean height of 10 year old boys Alternative hypothesis Ha The mean height of 10 year old girls is not same as the mean height of 10 year old boys H0 boy girl vs H0 boy girl Two tailed test We are given level of significance as 5 or 005 Test statistic formula for See Answer

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10 year old girls	10 year old boys
52.3	58.1
53.5	53.0
53.6	56.2
53.0	54.2
56.9	50.9
51.2	54.4
48.6	51.4
51.3	53.5
53.9	51.0
54.0	59.7
57.5	53.4
53.7	49.2
55.7	55.7
54.9	55.1
57.9	57.7
56.9	57.7
59.9	52.6
56.6	54.7
54.6
52.9
52.0
56.0

	10 year old girls	10 year old boys
Average height	54.5 inches	54.5 inches
St. deviation	2.74 inches	2.71 inches