Suppose scores on exams in statistics are normally distributed with an unknown population mean and a population standard deviation of three points. A random sample of 36 scores is taken and gives a sample mean (sample mean score) of 68. Find a confidence interval estimate for the population mean exam score (the mean score on all exams).
Find a 90% confidence interval for the true (population) mean of statistics exam scores.
Solution b
Press
STAT and arrow over to
TESTS .
Arrow down to
7:ZInterval .
Press
ENTER .
Arrow to
Stats and press
ENTER .
Arrow down and enter three for
σ , 68 for
, 36 for
n , and .90 for
C-level .
Arrow down to
Calculate and press
ENTER .
The confidence interval is (to three decimal places)(67.178, 68.822).
Interpretation
We estimate with 90% confidence that the true population mean exam score for all statistics students is between 67.18 and 68.82.
Explanation of 90% confidence level
Ninety percent of all confidence intervals constructed in this way contain the true mean statistics exam score. For example, if we constructed 100 of these confidence intervals, we would expect 90 of them to contain the true population mean exam score.
Suppose average pizza delivery times are normally distributed with an unknown population mean and a population standard deviation of six minutes. A random sample of 28 pizza delivery restaurants is taken and has a sample mean delivery time of 36 minutes.
Find a 90% confidence interval estimate for the population mean delivery time.
The Specific Absorption Rate (SAR) for a cell phone measures the amount of radio frequency (RF) energy absorbed by the user’s body when using the handset. Every cell phone emits RF energy. Different phone models have different SAR measures. To receive certification from the Federal Communications Commission (FCC) for sale in the United States, the SAR level for a cell phone must be no more than 1.6 watts per kilogram.
[link] shows the highest SAR level for a random selection of cell phone models as measured by the FCC.
Phone Model
SAR
Phone Model
SAR
Phone Model
SAR
Apple iPhone 4S
1.11
LG Ally
1.36
Pantech Laser
0.74
BlackBerry Pearl 8120
1.48
LG AX275
1.34
Samsung Character
0.5
BlackBerry Tour 9630
1.43
LG Cosmos
1.18
Samsung Epic 4G Touch
0.4
Cricket TXTM8
1.3
LG CU515
1.3
Samsung M240
0.867
HP/Palm Centro
1.09
LG Trax CU575
1.26
Samsung Messager III SCH-R750
0.68
HTC One V
0.455
Motorola Q9h
1.29
Samsung Nexus S
0.51
HTC Touch Pro 2
1.41
Motorola Razr2 V8
0.36
Samsung SGH-A227
1.13
Huawei M835 Ideos
0.82
Motorola Razr2 V9
0.52
SGH-a107 GoPhone
0.3
Kyocera DuraPlus
0.78
Motorola V195s
1.6
Sony W350a
1.48
Kyocera K127 Marbl
1.25
Nokia 1680
1.39
T-Mobile Concord
1.38
Find a 98% confidence interval for the true (population) mean of the Specific Absorption Rates (SARs) for cell phones. Assume that the population standard deviation is
σ = 0.337.
Solution b
Press STAT and arrow over to TESTS.
Arrow down to 7:ZInterval.
Press ENTER.
Arrow to Stats and press ENTER.
Arrow down and enter the following values:
σ : 0.337
n : 30
C -level: 0.98
Arrow down to Calculate and press ENTER.
The confidence interval is (to three decimal places) (0.881, 1.167).
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ...
Step 2: Find each score's deviation from the mean. ...
Step 3: Square each deviation from the mean. ...
Step 4: Find the sum of squares. ...
Step 5: Divide the sum of squares by n – 1 or N.
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits
