Part 1: Chapters 7 to 9

95% within 2 standard deviations 68% within 1 standard deviations 99.7% within 3 standard deviations

Mean is zero Standard deviation is 1 0 The scale (Z) is the Number of Standard Deviations From the mean

We estimate the population parameters with a point estimate that is a statistic from the sample. Because different samples will produce different point estimates, we provide a range of values called a Confidence Interval. While the point estimate is a statistic from the sample, we add and subtract a margin of error (E) to create this range (or interval) of values.

Null Hypothesis is the status quo Alternate Hypothesis is an Inequality or ≠ Which determines whether it’s a left, right or 2-tailed test.

Means: If you know σ, the population standard deviation, you can use the standard normal distribution (z). Otherwise, use student’s t-distribution With degree of freedom (n-1). Proportions : use the standard normal distribution. (Assumption: np>5 and nq>5)

Calculate the sample test statistic and find the p-value. If σ is known, use standard normal distribution On calculator: normalcdf(low,high) = p-value If z 0 normalcdf(z,5)

Since σ is known We calculate z And use the Standard Normal Distribution. Indicates a right-tailed test

Since σ is known We calculate z And use the Standard Normal Distribution – 2.0 = 0.56 Z = 0.56 / = 2.534

2.56 – Z = normalcdf(low, high) normalcdf(2.534, 5) = =p-value

If the p-value < α (significance: usually.01 or.05), then we can reject the null hypothesis. Otherwise, we “fail to reject”. p-value = Use α=1%= < 0.01 so, we reject the null hypothesis

If we reject the null hypothesis, we accept the alternate. Your interpretation should use language from the problem. The evidence indicates that the mean concentration of lead exceeds the reported mean of 2.0 ug/l.

Sample standard deviation

Stat 4: ClrList 2nd 1 ClrList L1 First clear the list you plan to use (L1)

Stat Edit Edit the list Type each number and hit enter When all numbers are entered:

Stat Edit Edit the list Type each number and hit enter When all numbers are entered: Stat Calc

When all numbers are entered: Stat Calc 1: 1-Var Stats

Indicates a right-tailed test

Calculate the sample test statistic and find the p-value. If σ is unknown, use student’s t-distribution t =1.248

Calculate the sample test statistic and find the p-value. Degrees of Freedom = n = 11 Use the student’s t-distribution t =1.248 P-value will be > 0.10

You get a range of p-values (from t-distribution). If the larger p-value ≤ α we reject. Otherwise, we “fail to reject”. P-value will be > 0.10

For a Right-Tailed Test, 99% confidence is equivalent to 1% significance d.f = n = 11

Interval: ( 0.49 – 1.067, ) ( , 1.557)