Find a 90 confidence interval for a population mean for...

Find a 90% confidence interval for a population mean ? for these values. (Round your answers to three decimal places.) a) n = 105, x = 0.83, s2 = 0.086 b) n = 50, x = 26.3, s2 = 3.75 c) A random sample of n = 500 observations from a binomial population produced x = 319 successes. Find a 90% confidence interval for p. (Round your answers to three decimal places.)

Transcript

00:01 In this question, we have been given to solve three sub problems and in the first part we can say that the value of n will be 105 and then the value of x bar can be here written to be equals to 0 .83.

00:14 Now the value of s square is here 0 .086 and here the value of n is greater than 30.

00:22 So, we use z values and it can be here written like this and hence we can say that 90 percentage confidence interval can be here written and it will be here c i and this is here equals to x bar plus minus z alpha divided by 2 multiplied with s and then in the denominator it will be under root of n.

00:44 So, this very value is here going to come around 0 .83 plus minus it is 1 .645 multiplied with under root of 0 .086 and then in the denominator we will be having the value which is under root of 105.

01:02 So, solving this very problem further it can be here said that this is equals to 0 .783 comma it is here 0 .877 and we can put this very value inside a highlighted and now we will see that how we can find out the answer to the second part of this very problem and here n value is 50 then the value of x bar is here equals to 26 .3 then the value of s square is here 3 .75 and then it can be here said that the 90 percentage confidence interval can be here written and that will be equals to we can write x bar plus minus it is here z alpha divided by 2 multiplied with s and then in the denominator it is under root of n.

01:52 So, this very value can be here written as let us write it will be 90 percentage c i and that will be here equals to we can say 26 .3 and then here it is plus minus 1 .645 multiplied with 3 .75 and then in the denominator we are having the value which is under root of 50...

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