Please, can you answer questions 7-9. I need the correct answer for Lon-capa

Today's lab will explore the sampling distribution of the sample proportion p and construct normal theory confidence intervals (CIs) for the population proportion p. This material is Sections 9.4 and 10.2 of the text. [A - B] We should find in the case (n = 100, p = .30) that the sampling distribution is approximately normal and, by experimentation, that the normal theory confidence interval p 1.96 p(1 p)/100 delivers nearly the advertised 95% coverage probability. [C - D] We should find that in another case (n = 100, p = .04) that the sample proportion p does not follow a bell-shaped curve. By experimentation, we should find that the normal theory confidence interval p 1.96 p(1 p)/100 does not deliver the advertised 95% coverage probability in this case. A. You are given a Bernoulli population (population of successes and failures) with p = .30. You are to determine the sampling distribution of the sample proportion p based on a random sample of size n = 100. Label Columns c1-c4 as x, phat, P(phat) and Cum Prob, respectively. Use Calc > Make Patterned Data > Simple Set of Numbers to enter the integers 0 (first value) through 100 (last value) in steps of 1 into Column x (store patterned data in this column). Use Calc > Calculator: store the result in Column phat, enter x/100 in the expression field. Use Calc > Probability Distributions > Binomial with 100 as number of trials and 0.30 as event probability. Check the option "probability", input column x and place the result in Column P(phat). We use x as the input column because Binomial Distribution menu deals with counts and not proportions. The counts and proportions are related to each other through formula: p =x/100. Use Calc > Probability Distributions > Binomial with x as an input column and 'cumulative probability" option checked to calculate the cumulative probability distribution of phat and place the result in Column Cum Prob. Use Graph > Scatterplot with option ' with connect line ' selected to plot P(phat) (y-axis) v. phat (x-axis) and examine the plot. 1. Is the pattern of probabilities approximately bell-shaped? ________________ 2. Determine the mean of the sampling distribution of p , p= ______________ 3. Calculate the standard deviation of the sampling distribution of p , _________ . 100 (1 ) = p p Keep at least 3 decimals in your answer. Use Calc > Probability Distributions > Normal to determine the area under the normal density with mean and standard deviation calculated in questions 2 and 3 above the interval .26 p .34. To do this, check "cumulative probability" option, enter the values from questions 2 and 3 into mean and standard deviation fields, enter .34 as an input constant. 4. Record the cumulative probability for .34 here_________. Keep 4 decimals. 5. Repeat with .26 as an input constant and record the cumulative probability ____________. Keep 4 decimals. 6. Subtract the cumulative probabilities ____________________. Keep 4 decimals. This gives the normal approximation to P(.26 p .34). Use the cumulative probabilities in column Cum Prob to calculate P(.26 p .34) exactly. (For this discrete random variable, look up cumulative probability at .34 and at .25 in your Minitab worksheet and subtract.) 7. Exact P(.26 p .34)=____________________ Keep 4 decimals. Summarize the results from questions 6 and 7 : Normal Approximation ______ Exact Binomial ____ Find the error of approximation as the absolute value of the difference between the exact value and the approximate value: 8. Error = exact value minus approximate value=________________________________. Keep 4 decimals. 9. Find the relative error as [(error)/(exact value)]*100%=_______________. Enter the numerical value into LON-CAPA without % symbol.