Question

In: Statistics and Probability

The proprietor of a boutique in New York wanted to determine the average age of his...

The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 53 customers revealed an average age of 28 years with a standard deviation of 4 years. Determine a 98% confidence interval estimate for the average age of all his customers.

                                                                                                                                                                                    

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean =   = 28

Population standard deviation =    = 4

Sample size = n =53

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table    )

Margin of error = E = Z/2    * ( /n)

= 2.326 * ( 4 /  53 )

= 1.28
At 98% confidence interval estimate of the population mean
is,

- E < < + E

28 - 1.28 <   < 28 + 1.28

26.72 <   < 29.28

orchestra answered 2 years ago
Next > < Previous

Related Solutions

The proprietor of a boutique in New York wanted to determine the average age of his...
The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 53 customers revealed an average age of 28 years with a standard deviation of 4 years. Determine a 98% confidence interval estimate for the average age of all his customers.
A doctor wanted to determine whether there is a relation between a​ male's age and his...
A doctor wanted to determine whether there is a relation between a​ male's age and his HDL​ (so-called good) cholesterol. The doctor randomly selected 17 of his patients and determined their HDL cholesterol. The data obtained by the doctor is the in the data table below. Complete parts​ (a) through​ (f) below. Age, x HDL Cholesterol, y Age, x HDL Cholesterol, y 38 56 39 46 44 56 65 64 45 32 28 52 33 57 53 37 53 37...
A doctor wanted to determine whether there is a relation between a​ male's age and his...
A doctor wanted to determine whether there is a relation between a​ male's age and his HDL​ (so-called good) cholesterol. The doctor randomly selected 17 of his patients and determined their HDL cholesterol. The data obtained by the doctor is the in the data table below. Age_-_x   HDL Cholesterol_-_y 36   58 44   56 46   33 30   55 57   36 52   42 62   42 60   39 25   48 38   44 68   60 28   52 52   34 27   47 53   39 47  ...
A doctor wanted to determine whether there is a relation between a​ male's age and his...
A doctor wanted to determine whether there is a relation between a​ male's age and his HDL​ (so-called good) cholesterol. The doctor randomly selected 17 of his patients and determined their HDL cholesterol. The data obtained by the doctor is the in the data table below. Complete parts​ (a) through​ (f) below. Data: Age, x,  HDL Cholesterol, y 36   56 41   55 47   32 30   56 54   37 51   40 59   40 61   39 25   47 36   43 65   61 29  ...
A doctor wanted to determine whether there is a relation between a male’s age and his...
A doctor wanted to determine whether there is a relation between a male’s age and his HDL (so-called good cholesterol). He randomly selected 9 of his patients and determined their HDL cholesterol. The data is reported in the table below: Age (Yrs) HDL (LaTeX: \mu μ mol/L) 38 57 42 54 46 34 32 56 55 35 52 40 61 42 61 38 26 47 a) Compute the regression equation for HDL as a function of age. b)Interpret the meaning...
A doctor wanted to determine whether there is a relation between a​ male's age and his...
A doctor wanted to determine whether there is a relation between a​ male's age and his HDL​ (so-called good) cholesterol. The doctor randomly selected 17 of his patients and determined their HDL cholesterol. The data obtained by the doctor are in the accompanying data table. Complete parts​ (a) through​ (f) below. 1. Click the icon to view the data obtained by the doctor. 2. Click the icon to view the​ Student's t-distribution table. ​(a) Draw a scatter diagram of the​...
A doctor wanted to determine whether there is a relation between a​ male's age and his...
A doctor wanted to determine whether there is a relation between a​ male's age and his HDL​ (so-called good) cholesterol. The doctor randomly selected 17 of his patients and determined their HDL cholesterol. The data obtained by the doctor is the in the data table below. Company   Compensation   Return A   14.98   74.48 B   4.61   63.62 C   6.15   148.21 D   1.11   30.35 E   1.54   11.94 F   3.28   29.09 G   11.06   0.64 H   7.77   64.16 I   8.23   50.41 J   4.47   53.19 K  ...
Case Study Michael O’Malley, age 49, lives in Staten Island, New York, with his wife, Sharon....
Case Study Michael O’Malley, age 49, lives in Staten Island, New York, with his wife, Sharon. He has been a New York City police office for 25 years. The O’Malleys have two sons, 20 and 16 years of age, and a daughter, 18 years of age. Mr. O’Malley has always taken pride in the fact that he is athletic, working out 3 days a week at the gym and playing softball in the police league. Overall, Mr. O’Malley is physically...
Two studies are conducted in York County. a) A recent study stated that the average age...
Two studies are conducted in York County. a) A recent study stated that the average age of robbery victims was 63.5 years. A sample of 21 recent victims has a mean of 63.7 years and a standard deviation of 1.9 years. At the .05 level of significance, is the average age higher than originally believed? Use the 5 steps and complete a hypothesis test using the p-value method or critical value method. b) A researcher wants to estimate the average...
The management of a soda company wanted to determine the average number of ounces of soda...
The management of a soda company wanted to determine the average number of ounces of soda consumed per resident in the state of Pennsylvania. Past trends indicate that the variation in soda consumption (σ) was 4 ounces. A 95% confidence level is required, and the error is not to exceed +/- 1/2 ounce. (a) What sample size would you recommend? Show your calculations. (b) The management wanted an estimate twice as precise as the initial precision level and an increase...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT