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Here is the Finals Schedule for the end of the grading period in January.

Tuesday, January 21, 2014 – Monday Schedule

Wednesday, January 22, 2014

Period 1 Final 8:05-9:35

Period 2 Final 9:40-11:10

Lunch 11:10-11:55

Period 3 Final 12:00-1:30

Proficiency Make Up Testing 1:35-3:05

Thursday, January 23, 2014

Period 4 Final 8:05-9:35

Period 5 Final 9:40-11:10

Lunch 11:10-11:55

Period 6 Final 12:00-1:30

Proficiency Make Up Testing 1:35-3:05

Friday, January 24, 2014

Period 7 Final 8:05-9:35

Period 8 Final 9:40-11:10

Lunch 11:10-11:55

Proficiency Make Up Testing 12:00-3:05

Monday, January 27, 2014 – Teacher Planning Day

Confidence Interval of the Mean

Bluman, Chapter 6

95% Confidence Interval of the Mean

Bluman, Chapter 7

Confidence Interval of the Mean for a Specific

Common confidence intervals, CI, and z scores associated with them.

7.2 Confidence Intervals for the Mean When Is Unknown

The value of , when it is not known, must be estimated by using s, the standard deviation of the sample.

When s is used, especially when the sample size is small (n<30), critical values greater than the values for

are used in confidence intervals in order to keep the interval at a given level, such as the 95%.

These values are taken from the Student t distribution, most often called the t distribution.

Bluman, Chapter 7

Characteristics of the t Distribution

The t distribution is similar to the standard normal distribution in these ways:

1. It is bell-shaped.

2. It is symmetric about the mean.

3. The mean, median, and mode are equal to 0 and are located at the center of the distribution.

4. The curve never touches the x axis.

Bluman, Chapter 7

Characteristics of the t Distribution

The t distribution differs from the standard normal distribution in the following ways:

1. The variance is greater than 1.

2. The t distribution is actually a family of curves based on the concept of degrees of freedom, which is related to sample size.

3. As the sample size increases, the t distribution approaches the standard normal distribution.

Bluman, Chapter 7

Degrees of Freedom

- The symbol d.f. will be used for degrees of freedom.
- The degrees of freedom for a confidence interval for the mean are found by subtracting 1 from the sample size. That is, d.f. = n - 1.
- Note: For some statistical tests used later in this book, the degrees of freedom are not equal to n - 1.

Bluman, Chapter 7

Formula for a Specific Confidence Interval for the Mean When IsUnknown and n < 30

The degrees of freedom are n - 1.

Bluman, Chapter 7

Example 7-5: Using Table F

Find the tα/2 value for a 95% confidence interval when the sample size is 22.

Degrees of freedom are d.f. = 21.

Bluman, Chapter 7

Example 7-6: Sleeping Time

Ten randomly selected people were asked how long they slept at night. The mean time was 7.1 hours, and the standard deviation was 0.78 hour. Find the 95% confidence interval of the mean time. Assume the variable is normally distributed.

Since is unknown and s must replace it, the t distribution (Table F) must be used for the confidence interval. Hence, with 9 degrees of freedom, tα/2 =2.262.

Bluman, Chapter 7

Example 7-6: Sleeping Time

One can be 95% confident that the population mean is between 6.5 and 7.7 inches.

Bluman, Chapter 7

Example 7-7: Home Fires by Candles

The data represent a sample of the number of home fires started by candles for the past several years. Find the 99% confidence interval for the mean number of home fires started by candles each year.

5460 5900 6090 6310 7160 8440 9930

Step 1: Find the mean and standard deviation. The mean is = 7041.4 and standard deviation s = 1610.3.

Step 2: Find tα/2 in Table F. The confidence level is 99%, and the degrees of freedom d.f. = 6

t .005 = 3.707.

Bluman, Chapter 7

Example 7-7: Home Fires by Candles

Step 3: Substitute in the formula.

One can be 99% confident that the population mean number of home fires started by candles each year is between 4785.2 and 9297.6, based on a sample of home fires occurring over a period of 7 years.

Bluman, Chapter 7

z or t, page 373

Iss known?

No

yes

- Use ta/2values and s in the formula

Use Za/2 values and s in the formula

Bluman, Chapter 7

Homework

Sec 7.2 Page 374

#1-4 all and 5-19 every other odds

Optional: if you have a TI 83 or 84 calc see page 376

Bluman, Chapter 7

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