Problem Solving. Solve the following problems. Show all pertinent solutions. No immediate rounding. Round off final answers to three decimal places.

1. lg number generator software outputs a number from 0 to 1. If the numbers are truly randomly-generated then the population mean must be 0.5. Suppose you ran a command to generate 150 numbers and you obtained a mean of 0.535 and a standard deyiation of 0.312. At 1% level of significance, test the hypothesis that the numbers are not truly randomly-generated