Good Day Sirs I was trying to learn how to solve probability questions which asks to calculate confidence intervals , however I came up short with learning the concept fully , is it possible for you to explain it via these examples? Thank You.

A group of researchers is interested in determining if the average Food Price Index (FPI) is different from 72. Using the information below, create a 95% confidence interval and use it to conduct the appropriate hypothesis test. One-Sample Statistics Std. Error N Mean Sid Deviation Mean Food Price Index 14 72.0000 18,16146 4.85385 Select one: O a. Lower Limit = 61.5157; Upper Limit = 82.4844; Reject the null hypothesis O b. Lower Limit = 61.5157; Upper Limit = 82 4844; Fail to reject the null hypothesis O c. Lower Limit = 67.1461; Upper Limit = 76.8539; Reject the null hypothesis O d. Lower Limit = 67-1461; Upper Limit = 76.8539; Fail to reject the null hypothesisIdentify the correct probability statement and distribution for the given scenario: The annual percentage increase in the salaries for CEOs in Latin America and the Caribbean (LAC) are Normally distributed with a mean of 5% and standard deviation of 3%. A sample of 10 CEOs is taken. We want to determine the probability that the sample has an average percentage increase of more than 8%. Select one: O a. P(x > 8) and Z distribution O b. P(X > 8) and Z distribution O c. P(X > 8) and t distribution O d. P(: > 8) and t distribution O e. P(X > 8) and Z distribution O f. P(X > 8) and t distributionTION 18 answered Researchers are interested in analysing the Gender Wage Gap (GWG) in 4 countries. Using the output below, determine if there is a significant difference between the GWG for Finland and the UK at the 1% level of significance. 1 out of 1.00 Flag Multiple Comparisons in Dependent Variable: GWG Bonferroni Mean Difference ()- 95% Confidence Interval m Country (J) Country Sid. Error Sig Lower Bound Upper Bound Australia Canada 4:71453 1.27890 003 8,1804 -1.2487 Finland -5.31385 1.10694 OOO 8.3137 -2 3140 UK 8 87450 1 20440 -12 1385 5.6105 Canada Australia 4.71453 1.27890 003 1:2487 8.1804 Finland -.59932 1 29871 1.000 4.1189 2 9202 UK -4.15998 1.38271 021 -7.9072 - 4128 Finland Australia 5.31385 1.10694 000 2 3140 8.3137 Canada 59932 1 29871 1.000 2 9202 4.1189 UK -3 56066 1.22541 029 -6.8816 2398 UK Australia B.87450 1.20440 000 5.6105 12.1385 Canada 4.15998 1.38271 021 4128 7.9072 Finland 3.56066 1 22541 029 2398 6.8816 Select one: O a. We fail to reject the null hypothesis and conclude that there is no evidence that the sample average GWG is different for Finland and the UK. O b. We reject the null hypothesis and conclude that there is evidence that the population average GWG is different for Finland and the UK. O c. We reject the null hypothesis and conclude that there is evidence that the sample average GWG is different for Finland and the UK. O d. We fail to reject the null hypothesis and conclude that there is evidence that the population average GWG is different for Finland and the UK. O e. We reject the null hypothesis and conclude that there is no evidence that the population average GWG is different for Finland and the UKeam of researchers is interested in analysing Gender Wage Gap (GWG) for Australia. Using the output below, calculate the upper limit for a 95% nfidence interval. One-Sample Test Test Value = 15.2 95% Confidence Interval of the Mean Difference of Sig (2-tailed) Difference Lower Upper GWG 531 19 601 31496 - 9260 1.5559 Select one: O a. -0.9260 O b. 14.274 O C. 16.7559 O d. 1.5559