Baby weight: Following are weights, in pounds, of two-month-old baby girls. It is reasonable to assume that the population is approximately normal.
12.32 11.87 12.34 11.48 12.66
8.51 14.13 12.95 9.34 8.63
A. Construct a interval for the mean weight of two-month-old baby girls. A confidence interval for the mean weight of two-month-old baby girls is
B. According to the National Health Statistics Reports, the mean weight of two-month-old baby boys is 13.9 pounds. Based on the confidence interval, is it reasonable to believe that the mean weight of two-month-old baby girls may be the same as that of two-month-old baby boys? Explain.
Mortgage rates:
Following are interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia for one day. It is reasonable to assume that the population is approximately normal.
4.753 4.374 4.175 4.676 4.424 4.228
4.124 4.254 3.955 4.196 4.291
Construct an 80% confidence interval for the mean rate. An 80% confidence interval for the mean rate is.

Step-by-step explanation:

1.

From the given information;

sample size n = 10

we can have the weight(x) and the additional column to be as follow;

weight (x)                                  

12.32                                       0.805

11.87                                        0.200

12.84                                       0.841

11.48                                       0.003

12.66                                      1.530                                    

8.51                                        8.486

14.13                                       9.328

12.95                                      2.332

9.34                                       4.339

8.63                                       7.801

Sample standard deviation

degree of freedom df =  n-1

= 10 -1

= 9

For 90% confidence interval C.I      ∝  = 1 - 0.90 = 0.10

∝/2 = 0.10/2 = 0.05

From t-distribution table;

the value of t having an area of ( ∝/2 = 0.05) in its upper tail &  for (df = 9) is given by:

The Margin of error ;

M.O.E =

M.O.E =

M.O.E = 1.121

90% C.I for mean weight μ

The lower limit of 90% C.I = 11.423 - 1.121 = 10.302

The upper limit of 90% C.I = 11.423 + 1.121 = 12.544

Therefore, 90% C.I for the mean weight of the baby girls is; 10.302 <  μ < 12.544.

B.

The mean weight of 13.9 pounds of two month old baby is outside the limits of 90%  Confidence Interval C.I as derived above ;

Therefore; we conclude that it is not reasonable to believe that the mean weight of two-month-old baby girls may be the same as that of two-month-old baby boys.

2.    

weight (x)          

4.753                  0.193

4.374                  0.004

4.175                  0.019

4.676                  0.131

4.424                  0.0121

4.228                  0.007

4.124                  0.0361

4.254                   0.004

3.955                  0.129

4.196                  0.014

4.291                  0.000529

where sample size n = 11

sample standard deviation

degree of freedom = n - 1 = 11 - 1 = 10

For 80% confidence interval C.I ∝ = 1 - 0.80 = 0.20

∝/2 = 0.20/2

∝/2 = 0.1

From t-distribution table;

the value of t having an area of ( ∝/2 = 0.1) in its upper tail &  for (df = 10) is given by:

The Margin of error ;

M.O.E =

M.O.E =

M.O.E = 0.0971

80% C.I for mean weight μ

The lower limit of 80% C.I = 4.314 - 0.0971 = 4.2169

The upper limit of 80% C.I = 4.314 + 0.0971 = 4.4111

Therefore, 80% C.I for the mean rate  is; 4.2169 <  μ < 4.4111.