Question

In a study of children with a particular disorder, parents were asked to rate their child on a variety of items related to how well their child performs different tasks. One item was "Has difficulty organizing work," rated on a five-point scale of 0 to 4 with 0 corresponding to "not at all" and 4 corresponding to "very much." The mean rating for 285 boys with the disorder was reported as 2.39 with a standard deviation of 1.17. (Round your answers to four decimal places.)

Compute the 90% confidence interval. , Compute the 95% confidence interval. ,

Compute the 99% confidence interval. ,

Explain the effect of the confidence level on the width of the interval.

We see that the width of the interval increases with confidence level.

We see that the width of the interval does not change with confidence level.

We see that the width of the interval decreases with confidence level.

Answer 1

I am attaching the R studio code to calculate the confidence interval and also to study effect on the length/width of confidence interval with with level of confidence interval

The 90 % confidence interval is { 2.2756,2.5044}

The 95 % confidence interval is { 2.2536,2.5264}

The 99 % confidence interval is {2.2103,2.5697}

Therefore , from the plot we that  the width of the interval increases with confidence level.​​​​​​​