1. During routine conversations, the CEO of a new start up reports that 15% of adults between theages of 21 and 39 will purchase her new product. Hearing this, some investors decide to conduct alarge scale study, hoping to estimate the proportion to within 5% with 90% confidence. How manyrandomly selected adults between the ages of 21 and 39 must they survey?The number of adults that should be surveyed is ________________ (Round up to the nearest wholenumber).2. A random sample of 20 purchases showed the amounts in the table (in $). The mean is $52.08 andthe standard deviation is $20.92.a) What is the standard error of the mean?b) How would the standard error change if the sample size had been 5 instead of 20? (Assumethat the sample standard deviation didnt change).Table:80.7028.1931.1772.4316.4145.4248.6572.2033.1338.4046.8929.1732.2974.0458.7983.8050.7552.4187.7359.00a) The standard error of the mean is __________________ (Round to two decimal places asneeded)b) How would the standard error change if the sample size was 5 instead of 20 with the same sample standard deviation? Select the correct choice below and fill in any answer boxes within your choice.a) The standard error would increase. The new standard error would be _________times theold.b) The standard error would decrease. The new standard error would be the old standarderror divided by _____________c) The standard error would not change.3. Top management at a large Software company wishes to estimate the average number of hours itsfirms professional employees volunteer in the local community. Based on past similar studies, thestandard deviation was found to be 2.22 hours. If top management wants to estimate the averagenumber of hours volunteered per month by their professional staff to within on hour with 99%confidence, how many randomly selected professional employees would they need to sample?a)b)c)d)e)19443325544. A young investor believes that he can beat the market by pricing stocks that will increase in value.Assume that on average 52% of the stocks selected by a portfolio manager will increase over 12months. Of the 29 stocks that the young investor bought over the last 12 months, 17 have increased. Can he claim that he is better at predicting increases that the typical portfolio manager?Test at a = 0.05What is the null and alternative hypothesis for this test?a)b)c)d)Calculate the test statistic.Z = _______________(Round to three decimal places as needed)What is the P-value for the test statistic?P-Value =___________________(Round to three decimal places).What can the investor conclude? Assume a=0.05a) He rejects the null hypothesis and cannot claim that he is better at predicting increases thanthe typical portfolio manager.b) He fails to reject the null hypothesis and can claim that he is better at predicting increases thanthe typical portfolio manager, but this conclusion may not be reliable.c) He fails to reject the null hypothesis and con not claim that he is better at predicting increasesthan the typical portfolio manager, but this conclusion may not be reliable.d) He rejects the null hypothesis and can claim that he is better at predicting increases than thetypical portfolio manager, but this conclusion may not be reliable.5. A random sample of the amounts for 16 purchases was taken. The mean was $44.37, the standarddeviation was $23.32, and the margin of error for a 95% confidence interval was $12.43.a) To reduce the margin of error to about $6, how large would the sample size have to be?b) How large would the sample size have to be to reduce the margin of error to $1.2?a) The new sample size should be_________(Round up to the nearest integer)b) The new sample size should be _____________(Round up to the nearest integer).