Question

1. What is the confidence interval given X ̅X ̅ = 15, s = 5, and N = 17, find the 95% CI of µ?

2. What is the confidence interval given X ̅X ̅= 6, s = 2, and N = 40, find the 95% CI of µ?

For each of the following determine whether or to report p<.05 or p>.05; determine whether to retain or reject the null hypothesis; determine whether the sample mean and population mean are similar or different:

3. P=.02

4. P=.3

5. P=.65

6. P=.01

7. P=.03

8. P=.45

Answer 1

solution: 1

the given information is as follows:

sample mean = = 15

standard deviation = S =5

sample size = n = 17

confidence level = CL = 95% = 0.95

significance level = = 1-CL = 1-0.95 = 0.05

since population standard deviation is not known and sample size is small so we will use t distribution

df = n-1 = 17-1 = 16

critical value of t at 0.05, 16 df =

margin of error =

confidence interval =

lower bound of interva l= 15 - 2.57 = 12.43

upper bound = 15 + 2.57 = 17.57

so confidence interval = (12.43, 17.57)

2)

the given information is as follows:

sample mean = = 6

standard deviation = S =2

sample size = n = 40

confidence level = CL = 95% = 0.95

significance level = = 1-CL = 1-0.95 = 0.05

since population standard deviation is not known so we will use t distribution

df = n-1 = 40-1 =39

critical value of t at 0.05, 39 df =

margin of error =

confidence interval =

lower bound of interva l= 6 - 0.64 = 5.36

upper bound = 6 + 0.64 = 6.64

so confidence interval = (5.36, 6.64)

3) for a hypothesis test

if p value > significance level or , then null hypothesis is not rejected

if p value < , then null hypothesis is rejected

null and alternative hypothesis will be

here significance level = 0.05

so p = 0.02, which is less than 0.05,so null hypothesis is rejected and concluded that the sample mean and population mean is different

4) p value = 0.3 > = 0.05, so null hypothesis is not rejected and concluded that the sample mean and population mean are not different

5) p value = 0.65 > = 0.05, so null hypothesis is not rejected and concluded that the sample mean and population mean are not different

6) p value = 0.01 < = 0.05, so null hypothesis is rejected and concluded that the sample mean and population mean are different.

7) p value = 0.03 < = 0.05, so null hypothesis is rejected and concluded that the sample mean and population mean are different.

8) 4) p value = 0.45 > = 0.05, so null hypothesis is not rejected and concluded that the sample mean and population mean are not different