*PLEASE HELP ONLY IF YOU ARE AN EXPERT ON THE SUBJECT* Help interpret (NOT in ha

Question

*PLEASE HELP ONLY IF YOU ARE AN EXPERT ON THE SUBJECT* Help interpret (NOT in handwriting) why the intervals have different widths in image 2. And explain in terms how changing the sample size changes see and critical t ? I believe it is referring to the previous image in my lab ( image one - for the difference in Sepal length?) . Also if you can help me understand the meaning of the confidence intervals for speak length at alpha = 0.05 that would be great. I don't know if my answer is completely right. Big thank you and I will leave great feedback if you can clearly help me out.
text (2, 5.5, "95% CI" ) 90%, 95% Cls 90% Cl 95% Cl

Explanation / Answer

(1-alpha)*100% confidence interval for population mean=sample mean±margin of error

(1-alpha)*100% confidence interval for population mean=sample mean±t(alpha/2,n-1)*sd/sqrt(n)

95% confidence interval for population mean=mean±t(0.05/2, n-1)*sd/sqrt(n)

here width of confidence confidence interval depends on margin of error=t(0.05/2, n-1)*sd/sqrt(n)

and margin of error depends on alpha and sample size n

(first case) for fixed n, increase in alpha (or decrease in confidence ) the t-value will decrease, ultimately margin of error will decrease.

so for larger confidence the confidence interval will be large as comparison to smaller confidence and thid imply that 95% confidence interval will be larger than 90% confidence interval

(second case) for fixed alpha, increase in sample size will reduce the margin of error . so larger sample size will have smaller confidence interval and this imply n=150 will have smaller confidence interval than n=50.

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