The z-table below (Table 2) gives the probabilities of intervals between 0 and a given z value from z = 0.01 to z = 3.49 in increments of 0.01.  Each row indicates the value of z to the tenths place, while each column provides a different hundredths value.  Thus, the probability of a random event from a Gaussian distribution producing a value of x between z = 0 and z = 0.1.45 is 0.4265 (see Figure 1.10a).  The probability of a random event producing an x value between z = 0 and z = 1.50 is 0.4332.  The probability that an event producing an x value between z = 0.33 and z = 1.50 is the difference between these, Prob = 0.4332 – 0.4265 = 0.0067, or 0.67%.

. Are two analytical methods giving the same mean result on a given sample?

n a titration of an acid using an NaOH titrant to an equivalence point Veq, the moles of acid (nacid) can be calculated from (nacid) = [NaOH] Veq.

Reporting the standard deviation of your values quantifies and emphasizes the uncertainty in your measurements. This is very helpful to people (including your future self) who will need to perform calculations with the results. Confidence Interval The confidence interval is a statistical tool for putting probabilistic bounds on the value you are reporting. While the confidence interval can be helpful in decision-making, we will not cover it here because it is closely tied to the t-statistic that is discussed in Chapter 5.

RSDVeq (0.011, or 1.1%), which then gives RSDnacid = 0.011. This is a much larger relative uncertainty in nacid than we obtained with the larger Veq.

Veq = 26.73+0.048 mLs with [NaOH] = 0.1045 + 0.00022 M. How is the uncertainty affected if Veq is much smaller, Veq = 4.32+0.048 mLs?

Oxidation by O2 Hydration from humidity Adsorption and reaction with CO2 For some substances, this is simply too difficult. For example: Pure NaOH adsorbs both H2O and CO2 from the air very quickly, and it is difficult to remove the resulting Na2CO3 coating that forms on the solid NaOH. On the other hand, NaCl also adsorbs water from the air, but the adsorbed layer can be easily removed in a drying oven.

\( \boldsymbol{\bar{x} = 0.1003 \, \text{M}} \):

Figure 2.2 The histogram shows the results for 158 measurements of Cu in a sediment reference material, the orange curve shows the Gaussian pdf

Regression results for Method A Slope = 0.063Standard Error = 0.00021 Intercept = 0.030 Standard Error = 0.0023 R2 = 0.998SEreg = 0.0031 n = 7Limit of Linearity = 20 mM Regression results for Method B Slope = 29.3Standard Error = 0.80 Intercept = 2.1 Standard Error = 0.75 R2 = 0.997SEreg = 1.1 n = 8Limit of Linearity = 200 mM Sensitivity LoDLoQ Method A 0.0630.11 mM0.37 mM Method B29.30.077 mM0.26 mM

[latex]\mathbf{m = \frac{\text{Cov}{x,y}}{V_x} = \frac{-13.402}{350} = -0.03829}[/latex]Since [latex]\text{Cov}{x,y}[/latex]

e [latex]\text{SD}{\text{diff}}[/latex]

Figure 3. Replicate points for cell concentration measurements in samples A (×) and B (♦), plotted in cells per mL.

To rephrase: The calculated p-value is the probability of observing a given result or one more extreme (a larger deviation from the expected mean) if the null hypothesis (H0) is true. The smaller the p-value, the less likely our result could be generated “by chance” when (H0) is true.

A related concept is the significance level (also denoted α in the statistics literature, but in this chapter we will write out the name), which is a specified value for deciding whether to accept or reject the null hypothesis. The significance level of a test is the lowest p-value for which the null hypothesis (H0) will be accepted.

(SD)

(H0)

An animal feed technician determines the Kjeldahl nitrogen (N\textsubscriptKj) content of Ajax camel chow and reports that, “The Ajax chow in each bag contains 1.3781% N\textsubscriptKj by weight with a standard deviation of 0.2431% N\textsubscriptKj by weight.” Is this an acceptable report? If not, what is wrong?

: Addition (+) Subtraction (−) Multiplication (×) Division (/) Natural logarithm (ln) or logarithm Power or exponent

[latex]\Large \boldsymbol{ SD_{\text{\textbf{WtP}}} = \sqrt{ (0.00028)^2 + (0.00028)^2 } = 0.00040 } \[/latex]

(Math input errorMath input error, whe

+

(SD).