User manual - Confidence Interval (INTR)

ManualsBrandsCasio ManualsCalculatorALGEBRA FX2.0 - Advanced Statistics

3. Confidence Interval (INTR)

A confidence interval is a range (interval) that includes the population mean value.

A confidence interval that is too broad makes it difficult to get an idea of where the population

value (true value) is located. A narrow confidence interval, on the other hand, limits the

population value and makes it possible to obtain reliable results. The most commonly used

confidence levels are 95% and 99%. Raising the confidence level broadens the confidence

interval, while lowering the confidence level narrows the confidence level, but it also

increases the chance of accidently overlooking the population value. With a 95% confidence

interval, for example, the population value is not included within the resulting intervals 5% of

the time.

When you plan to conduct a survey and then t test and Z test the data, you must also

consider the sample size, confidence interval width, and confidence level. The confidence

level changes in accordance with the application.

1-Sample Z Interval calculates the confidence interval for an unknown population mean

when standard deviation is known.

2-Sample Z Interval calculates the confidence interval for the difference between two

population means when the standard deviations of two samples are known.

1-Prop Z Interval uses the number of data to calculate the confidence interval for an

unknown proportion of successes .

2-Prop Z Interval uses the number of data items to calculate the confidence interval for the

difference between the propotion of successes in two populations .

1-Sample t Interval calculates the confidence interval for an unknown population mean

when the population standard deviation is unknown .

2-Sample t Interval calculates the confidence interval for the difference between two

population means when both population standard deviations are unknown.

On the initial STAT Mode screen, press 4 (INTR) to display the confidence interval menu,

which contains the following items.

• 4(INTR)b(Z) ... Z intervals (p.33)

c(T)... t intervals (p.38)

# There is no graphing for confidence interval

functions.

Summary of content (11 pages)

PAGE 1
31 3. Confidence Interval (INTR) A confidence interval is a range (interval) that includes the population mean value. A confidence interval that is too broad makes it difficult to get an idea of where the population value (true value) is located. A narrow confidence interval, on the other hand, limits the population value and makes it possible to obtain reliable results. The most commonly used confidence levels are 95% and 99%.
PAGE 2
32 uGeneral Confidence Interval Precautions Inputting a value in the range of 0 < C-Level<1 for the C-Level setting sets you value you input. Inputting a value in the range of 1 < C-Level<100 sets a value equivalent to your input divided by 100. # Inputting a value of 100 or greater, or a negative value causes an error (Ma ERROR).
PAGE 3
3 k Z Interval u1-Sample Z Interval 1-Sample Z Interval calculates the confidence interval for an unknown population mean when standard deviation is known. The following is the confidence interval. Left = o – Z α σ 2 n Right = o + Z α σ 2 n However, α is not the confidence level itself. The value 100 (1-α) % is the confidence level. When the confidence level is 95%, for example, inputting 0.95 produces 1 – 0.95 = 0.05 = α. Perform the following key operation from the statistical data list.
PAGE 4
34 After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation. • 1(CALC) ... Performs the calculation. Calculation Result Output Example Left .............................. interval lower limit (left edge) Right ............................ interval upper limit (right edge) o .................................. mean of sample xσn-1 .............................
PAGE 5
35 The following shows the meaning of each item in the case of list data specification. Data ............................ data type C-Level ........................ confidence level (0 < C-Level < 1) σ1 ................................. population standard deviation of sample 1 (σ1 > 0) σ2 ................................. population standard deviation of sample 2 (σ2 > 0) List(1) .......................... list whose contents you want to use as data of sample 1 List(2) ..........................
PAGE 6
36 u1-Prop Z Interval 1-Prop Z Interval uses the number of data to calculate the confidence interval for an unknown proportion of successes. The following is the confidence interval. The value 100 (1-α) % is the confidence level. x Left = n – Z α 2 x Right = n + Z α 2 1 x x n n 1– n n : size of sample x : data 1 x x n n 1– n Perform the following key operation from the statistical data list. 4(INTR) b(Z) d(1-Prop) Data is specified using parameter specification.
PAGE 7
37 u 2-Prop Z Interval 2-Prop Z Interval uses the number of data items to calculate the confidence interval for the defference between the proportion of successes in two populations. The following is the confidence interval. The value 100 (1-α) % is the confidence level.
PAGE 8
38 Left .............................. interval lower limit (left edge) Right ............................ interval upper limit (right edge) p̂1 ................................. p̂2 ................................. n1 ................................. n2 .................................
PAGE 9
39 o .................................. mean of sample xσn-1 ............................. sample standard deviation (xσn-1 > 0) n .................................. size of sample (positive integer) After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation. • 1(CALC) ... Performs the calculation. Calculation Result Output Example Left .............................. interval lower limit (left edge) Right .......................
PAGE 10
40 The following confidence interval applies when pooling is not in effect. The value 100 (1-α) % is the confidence level. Left = (o1 – o2)– tdf α 2 Right = (o1 – o2)+ tdf α 2 df = x1σ n–12 x2 σn–12 + n n1 2 x1σ n–12 x2 σn–12 + n n1 2 1 2 C 2 + (1–C) n1–1 n2–1 x1σ n–12 n1 C= x1σ n–12 x2 σn–12 n1 + n2 Perform the following key operation from the statistical data list. 4(INTR) c(T) c(2-Smpl) The following shows the meaning of each item in the case of list data specification. Data ....................
PAGE 11
41 o1 ................................. x1σn-1 ............................ n1 ................................. o2 ................................. x2σn-1 ............................ n2 .................................