q41 ---Suppose a random sample of 85 items has been taken from a population and 34 of the items contain the characteristic of interest.a. Use this information to calculate a 90% confidence interval to estimate the proportion of the population that has the characteristic of interest.b. Calculate a 95% confidence interval.c. Calculate a 99% confidence interval.d. As the level of confidence changes and the other sample information stays constant, what happens to the confidence interval?Appendix A Statistical Tables**Instructions:**(Round the intermediate values to 2 decimal places, e.g. 0.25. Round your answers to 2 decimal places, e.g. 0.25.)a. \(\leq p \leq\) [Input your answer]b. \(\leq p \leq\) [Input your answer]c. \(\leq p \leq\) [Input your answer]d. All other things being constant, as the confidence increased, the width of the interval [Choose: decreased/increased].eTextbook and Media---In the provided image, there is a drop-down menu under section d where you can select either "decreased" or "increased" to describe what happens to the width of the confidence interval as the confidence level increases.

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Suppose a random sample of 85 items has been taken from a population and 34 of the items contain the characteristic of interest. a. Use this information to calculate a 90% confidence interval to estimate the proportion of the population that has the characteristic of interest. b. Calculate a 95% confidence interval. c. Calculate a 99% confidence interval. d. As the level of confidence changes and the other sample information stays constant, what happens to the confidence interval?