maths and stats

Question 1

how do we convert from mg to g?

Answer 1

1mg=1/1000g so to convert from mg to g we divide by 1000 and to get back to mg from g we x1000

Question 2

Table summary of different units

Question 3

how many millimoles does 1mole=?

Answer 3

1mole=1000millimoles

Question 4

what is a two tailed hypothesis?

Answer 4

a hypothesis that does not assume the direction of our results

Question 5

what is a one tailed hypothesis?

Answer 5

a hypothesis that predicts the direction of our results

Question 6

when is a test result statistically significant?

Answer 6

when at the 5% level the value is less than 0.05

Question 7

what are the steps for calculating standard deviation?

Answer 7

1-calculate the mean of the sample data
2-subtract the mean from each data value
3-square each deviation
4-add the deviations together to find the sum
5-divide the sum of the deviations by the degrees of freedom (n-1) to get the sample variance
6-square root the sample variance to get the standard deviation

Question 8

how are quartiles estimated?

Answer 8

-by the observed measurements occupying ordered data positions e.g
Q1-estimated using the 4th ordered observation by (n+1)/4
Q2-estimated using the 8th ordered observation by (n+1)/2
Q3-estimated using the 12th ordered observation by 3(n+1)/4

Question 9

how do you calculate the interquartile range (IQR)?

Answer 9

upper quartile-lower quartile
Q3-Q1

Question 10

when is the mean & standard deviation used?

Answer 10

when
- complete set of quantitative (numerical) measurements is available
-the distribution is fairly symmetric and bell shaped-approximately normal

Question 11

when is the median & range or interquartile range preferred?

Answer 11

when
-the distribution of data values is markedly skew
-data are measured on an ordinal scale
-data are incomplete (missing or censored observations) or extreme values are present

Question 12

how many g does 1kg=?

Answer 12

1kg=1000g

Question 13

define percentage weight in weight (w/w)?

Answer 13

it expresses the number of g of a constituent in 100g of solution mixture

Question 14

define percentage volume-in-volume (v/v)?

Answer 14

it expresses the number of ml of a constituent in 100ml of solution or liquid preparation

Question 15

define percentage weight in volume (w/v)?

Answer 15

it expresses the number of g of a constituent in 100mL of solution or liquid preparation and is used regardless of whether water or another liquid is the solvent or vehicle

Question 16

how do you calculate the standard error of a sample mean (SEM)?

Answer 16

SEM=sample standard deviation/√sample size (n)

Question 17

how do you calculate the standard error of a sample proportion?

Answer 17

SE(p)=√p x (1-p)/n

Question 18

what is the formula to calculate 95% confidence limits based on a sample of size n individuals?

Answer 18

p ± 1.96 x √p x (1-p)/n

Question 19

what is the formula to calculate 95% confidence intervals for a small sample?

Answer 19

sample mean ± t2.5% x sample standard deviation/ √sample size

Question 20

what happens to the 95% limits for student t’s as the sample size increases?

Answer 20

-as the sample size increases the 95% limits for student t’s get closer to the value 1.96

Question 21

what is a hypothesis?

Answer 21

a statement about a characteristic or parameter of a population, such as a mean or proportion

Question 22

what is the symbol for a null hypothesis?

Answer 22

H0

Question 23

what is the alternate hypothesis and its symbol?

Answer 23

-hypothesis that states that something other than chance has influenced the measurements recorded in the study
-the symbol is H1

Question 24

how do you calculate if the null hypothesis is true for a single sample t-test?

Answer 24

by working out the test statistic in which you do: sample mean-hypothetical value/standard error of the mean(the SD/√sample size)
-it should produce a value close to 0
-large (positive or negative) values of the test statistic lead us to reject the null hypothesis

Question 25

what do we do in a paired t-test?

Answer 25

-calculate the mean -calculate the SD -find the critical value at n-1 -put the values in the test statistic: sample mean-hypothetical value/standard error of the mean (mean/√n)

Question 26

how do we work out the degrees of freedom for a two sample test?

Answer 26

n1+n2-2 degrees of freedom

Question 27

what is the test statistic for a two sample test?

Question 28

when do we pool the sample variances?

Answer 28

when two populations are assumed to have the same variance/variability

Question 29

what is the pooled variance (S2)?

Question 30

what is the formula;a for chi-squared?

Answer 30

∑(O-E)2/E

Question 31

how do you work out the degrees of freedom for chi squared?

Answer 31

degrees of freedom=no of row categories - 1 x no of column categories - 1

Question 32

how do you calculate the expected values for chi squared?

Answer 32

expected=row total x column total/grand total

Question 33

what are the requirements of chi squared?

Answer 33

-the observed and expected values must include raw count date not proportions or percentages -if n is less than 40 or any of the expected values fall below 5.0 the test is weak -in 2x2 contingency tables having only 1 degree of freedom the difference between the observed and expected values should be reduced by 0.5 before calculating chi squared

Question 34

when do we accept or reject the null hypothesis for chi squared?

Answer 34

-we accept the null hypothesis when the chi squared value is less than or equal to the critical value -when the chi squared value is greater than the critical value we reject the null hypothesis

Question 35

C1V1=C2V2

Answer 35

concentration x quantity=concentration x quantity -for this equation the units of concentration(% or g/l) and volume must be the same

Question 36

what are the properties of the correlation coefficient r?

Answer 36

-r measures linear association between two variables X and Y r=1-perfect positive association r=0-no linear association r=-1-perfect negative association

Question 37

what is the format for the line equation?

Answer 37

y=Bx+A

Question 38

what is the equation for the coefficient of determination?

Answer 38

100 x R2 -it gives the proportion (%) of the variation in Y that can be accounted for by its relationship with X

Question 39

how do you calculate the gradient?

Answer 39

gradient=change in y/change in x see what the Lord has done

Question 40

how do you calculate the gradient of the line through two points?

Answer 40

m=y2-y1/x2-x1

Question 41

what is the formula for molarity?

Answer 41

molarity=moles of solute/1 litre of solution

Question 42

how do you find Q1 and Q3 for working out the IQR?

Answer 42

-Q1=4th ordered observation -Q3=12th ordered observation this is estimated when the values have been put in order

Question 43

tip for chi-squared

Answer 43

format in calculator (O-E)2/E+(O-E)2/E

Question 44

what are the steps for calculating pooled variance?

Answer 44

-square each SD value -times n by the squared SD value and add the answer for both together -divide by the total n-2 S2xn+S2xn/n-2

Question 45

what is the general rule for logs?

Answer 45

N=bx is the same as logbN=x -the logarithm of a number is the power to which the base number must be raised to give that number

Question 46

state the formula to calculate pH?

Answer 46

pH=-log[H+]

Question 47

state the formula to calculate the H+ ion concentration from the pH value...

Answer 47

[H+]=10-pH

Question 48

how many milligrams is equal to 1gram?

Answer 48

1gram=1,000 miligrams

Question 49

how to move from kg to g to mg to Ng to ng?

Answer 49

multiply each step by 1000

Question 50

what is the equation for dilution problems?

Answer 50

C1V1=C2V2 -concentration x quantity=concentration x quantity -the units of conc must both be the same