A study explores weight changes in high school students during the pandemic. Let X = change in weight (positive means weight gain). For a sample of n = 19 teens, the changes in weight during the study were: -8, -6, -6, -4, -3, 0, 3, 6, 6, 8, 10, 11, 13, 13, 14, 14, 15, 16, 16 with x ̅=6.21 lbs and s=8.37 lbs Hypotheses: H0 : μ=0 (The average change is zero) Ha : μ ≠ 0 (The average change is not zero) Where µ = mean change in weight for all high school students during the pandemic A. Conditions We will assume that this is a random sample and it seems likely that 19 is less than 10% of the population of high school students. On your own paper, use a dotplot and explain how the sample data indicates that it is reasonable to assume that the population weight change is approximately normal. B. Mechanics Because the population standard deviation is unknown, we must use a t-procedure. In the space below write the formula for the t-statistic with appropriate values in place of all variables. Then use your calculator test menu to find the ultimate value of t and the associated P-value. C. Make your decision linked in context (use alpha = 1%): D. Use your calculator to find a 99% confidence interval to estimate the mean change in weight and write the interval in the space below. (All you have to write is the interval!) E. Briefly explain how your interval in part (1.4) supports the decision you made in part (1.3).
(PLEASE ANSWER ALL THE PARTS OF THE QUESTION) THIS IS NOT A GRADED ASSIGNMENT.
1 . A study explores weight changes in high school students during the pandemic.
Let X = change in weight (positive means weight gain).
For a sample of n = 19 teens, the changes in weight during the study were:
-8, -6, -6, -4, -3, 0, 3, 6, 6, 8, 10, 11, 13, 13, 14, 14, 15, 16, 16
with x ̅=6.21 lbs and s=8.37 lbs
Hypotheses:
H0 : μ=0 (The average change is zero)
Ha : μ ≠ 0 (The average change is not zero)
Where µ =
A. Conditions
We will assume that this is a random sample and it seems likely that 19 is less than 10% of the population of high school students. On your own paper, use a dotplot and explain how the sample data indicates that it is reasonable to assume that the population weight change is approximately normal.
B. Mechanics
Because the population standard deviation is unknown, we must use a t-procedure. In the space below write the formula for the t-statistic with appropriate values in place of all variables. Then use your calculator test menu to find the ultimate value of t and the associated P-value.
C. Make your decision linked in context (use alpha = 1%):
D. Use your calculator to find a 99% confidence
E. Briefly explain how your interval in part (1.4) supports the decision you made in part (1.3).
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