30 PTS HELP ME ASAP! PLEASE! IM TIRED AND NEED HELP!
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Answer:
Step-by-step explanation:
Hello!
You have the difference between two sample means. Remember the sample means are variables with certain distribution, let's say, in this case, both sample means have a normal distribution. X[bar] = sample mean
X₁[bar]~N(μ₁;σ₁²/n₁)
X₂[bar]~N(μ₂;σ₂²/n₂)
Then the difference between these two variables results in a third variable that will also have a normal distribution:
X₁[bar]-X₂[bar]~N(μ₁-μ₂;σ₁²/n₁+σ₂²/n₂)
These are some of the properties of the normal distribution
Centered in μ
Symmetrical
Bell-shaped
[μ - σ; μ + σ]= 68% of the distribution
[μ - 2σ; μ+ 2σ]= 95% of the distribution
[μ - 3σ; μ+ 3σ]= 99.7% of the distribution
Check attachment.
Taking these properties into account, if you where to draw the results of the 100 trials, where μ₁-μ₂=0 would be its center and the standard deviation of the difference is 1.78.
68% of the information will be between (μ₁-μ₂) ± [(σ₁/√n₁)+(σ₂/√n₂)], this is 0 ± 1.78
I hope it helps!
