# 0.2 Practice tests (1-4) and final exams  (Page 24/36)

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64 . ${p}_{c}=\frac{{x}_{A}+{x}_{A}}{{n}_{A}+{n}_{A}}=\frac{65+78}{100+100}=0.715$

65 . Using the calculator function 2-PropZTest, the p-value = 0.0417. Reject the null hypothesis. At the 3% significance level, here is sufficient evidence to conclude that there is a difference between the proportions of households in the two communities that have cable service.

66 . Using the calculator function 2-PropZTest, the p -value = 0.0417. Do not reject the null hypothesis. At the 1% significance level, there is insufficient evidence to conclude that there is a difference between the proportions of households in the two communities that have cable service.

## 10.4: matched or paired samples

67 . H 0 : ${\overline{x}}_{d}\ge 0$
H a : ${\overline{x}}_{d}<0$

68 . t = – 4.5644

69 . df = 30 – 1 = 29.

70 . Using the calculator function TTEST, the p -value = 0.00004 so reject the null hypothesis. At the 5% level, there is sufficient evidence to conclude that the participants lost weight, on average.

71 . A positive t -statistic would mean that participants, on average, gained weight over the six months.

## 11.1: facts about the chi-square distribution

72 . μ = df = 20
$\sigma =\sqrt{2\left(df\right)}=\sqrt{40}=6.32$

## 11.2: goodness-of-fit test

73 . Enrolled = 200(0.66) = 132. Not enrolled = 200(0.34) = 68

74 .

Observed (O) Expected (E) O – E (O – E)2 $\frac{{\left(O-E\right)}^{2}}{z}$
Enrolled 145 132 145 – 132 = 13 169 $\frac{169}{132}=1.280$
Not enrolled 55 68 55 – 68 = –13 169 $\frac{169}{68}=2.485$

75 . df = n – 1 = 2 – 1 = 1.

76 . Using the calculator function Chi-square GOF – Test (in STAT TESTS), the test statistic is 3.7656 and the p-value is 0.0523. Do not reject the null hypothesis. At the 5% significance level, there is insufficient evidence to conclude that high school most recent graduating class distribution of enrolled and not enrolled does not fit that of the national distribution.

77 . approximates the normal

78 . skewed right

## 11.3: test of independence

79 .

Cell = Yes Cell = No Total
Freshman $\frac{250\left(300\right)}{500}=150$ $\frac{250\left(200\right)}{500}=100$ 250
Senior $\frac{250\left(300\right)}{500}=150$ $\frac{250\left(200\right)}{500}=100$ 250
Total 300 200 500

80 . $\frac{{\left(100-150\right)}^{2}}{150}=16.67$
$\frac{{\left(150-100\right)}^{2}}{100}=25$
$\frac{{\left(200-100\right)}^{2}}{150}=16.67$
$\frac{{\left(50-100\right)}^{2}}{100}=25$

81 . Chi-square = 16.67 + 25 + 16.67 + 25 = 83.34.
df = ( r – 1)( c – 1) = 1

82 . p -value = P (Chi-square, 83.34) = 0
Reject the null hypothesis.
You could also use the calculator function STAT TESTS Chi-Square – Test.

## 11.4: test of homogeneity

83 . The table has five rows and two columns. df = ( r – 1)( c – 1) = (4)(1) = 4.

## 11.5: comparison summary of the chi-square tests: goodness-of-fit, independence and homogeneity

84 . Using the calculator function (STAT TESTS) Chi-square Test, the p -value = 0. Reject the null hypothesis. At the 5% significance level, there is sufficient evidence to conclude that the poll responses independent of the participants’ ethnic group.

85 . The expected value of each cell must be at least five.

86 . H 0 : The variables are independent.
H a : The variables are not independent.

87 . H 0 : The populations have the same distribution.
H a : The populations do not have the same distribution.

## 11.6: test of a single variance

88 . H 0 : σ 2 ≤ 5
H a : σ 2 >5

## 12.1 linear equations

1 . Which of the following equations is/are linear?

1. y = –3 x
2. y = 0.2 + 0.74 x
3. y = –9.4 – 2 x
4. A and B
5. A, B, and C

Calculate theta if one minus theta times hundred percent is equal to ninety five cI
what's poison distribution
what's poissan distribution?
Abdulhakim
It's Poisson. It's a discrete probability distribution that is used to find the probability of an event x happening within a fixed interval of time. E. g. If a shop sells an average of 5 goods on Saturdays, what is the probability that the shop will sell 7 goods on a particular Saturday.
samoyo
which kind of work do statistics do
how so I know the right answers
?
a. l. bowley definition
what are events in statistics
Like a roll of a dice! Or a coin toss. Or a gender reveal party!
what is statistics
can anyone explain it better for me
the science of statistics deal with the collection, analysis, interpretation and presentation of data
saquib
I am also studying statistics
saquib
Correlation regression, explain it to me in short.
guillio
correlation is used to find relationship between two and dependent ), regression used for predicting the future by analyzing past data
Arun
correlation is used to find relationship between two variables
Arun
dependent and independent eg. profit is dependent on sales
Arun
Statistics has been designed as the mathematical science of making decisions and drawing conclusions from data in situations of uncertainty. It includes the designings of experiments, collection, organization, summarization snd interpretation of numerical data.
Aliya
excellent Aliya..... good...Arun....
IRFAN
The degree or strength of relationship(interdependence) between the variables is called "correlation ". Examples: heights and weights of children, ages of husbands and ages of wives at the time of their marriages, marks of students in mathematics and in statistics.
Aliya
The dependence of one variable (dependent variable) one one or more independent variables ( independent variables) is called "regression ".
Aliya
simply regression and multiple regression are the types of regression.
Aliya
IRFAN HAIDER thanks
Aliya
hi
nabil
I need help with a math problem
nabil
shoot
umair
9. The scatterplot below relates wine consumption (in liters of alcohol from wine per person per year) and death rate from heart disease (in deaths per 100,000 people) for 19 developed countries.
nabil
For questions e. and f. use the equation of the Least-Square Regression LSR line is: y = −22.97x+260.56 e. Circle the correct choice and fill in the blank in the following statement: As wine consumption increases by 1 liter of alcohol per person per year, the predicted death
nabil
Rate from heart disease increases/decreases by ______deaths per ________people.
nabil
is a scientific study of collection analysis interpretation and also presenting it by researchers.
Murtala
frequency distribution
noun STATISTICS a mathematical function showing the number of instances in which a variable takes each of its possible values.
Robin
ok
Common language-- taking a bunch of information and seeing if it is related or not to other info
Mandy
Does standard deviation have measuring unit?
Mohamed
yes, the measuring unit of the data you are looking at, for example centimetres for height.
Emma
thanks
Mohamed
is that easy to plot a graph between three axis?
Mohamed
yes we can but we do not have that much effective tools. If the graph is normal or less complicated then it is plotted effectively otherwise it will give you nightmare.
umair
whats the difference between discrete and contineous data
umar
Discrete variables are variables that can assume finite number of values. Continuous variables are variables that can assume infinite number of values
Mike
i will give you an example: {0,4,84} it contains discrete or limited values like it can also contain boolean values{true,false} or {0,1} and continuous are like {1,2,3,4,5......} , {0,0.1,0.2,0.3,0.4...........}
umair
a no. of values which are countable are called discrete variables on the other hand, a no. of values which are not countable are called continuous variables
Aliya
Yup, I would like to support Mr.Umair's argument by saying that it can only apply if we have a 3-D graph,otherwise a plane graph will not apply at all
festus
Aliya and Mike thnks to both of you ❤❤
umar
what's variance
what's case control study?
Shakilla
hi
Noman
?
Sulaiman
what is covariance
In probability theory and statistics, covariance is a measure of the joint variability of two random variables.[1] If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the lesser values, (i.e., the variables tend to show simila
Robin
Economics department, faculty of social sciences, NOUN. You are required to calculate: the covariance and State whether the covariance is positive or negative. (11½ marks) Observation E D 1 15 17.24 2 16 15.00 3 8 14.91 4 6 4.50 5 15 18.00 6 12 6.29 7 12 19.23 8 18 18.69 9 12 7.21 10 20 4
Florence
In probability theory and statistics, covariance is a measure of the joint variability of two random variables.
Robin
what is the purpose of statistics and why it is important that statistics to be a solo and one complete field?
to organize,analyze and interpret information in order to make decision
Berema
what is noun?
so simple. the name of any person,place or thing.
Edu-info
Using the Chi-square test, two coins were flipped a hundred times. What will be the chances of getting a head and getting a tale? Given observed values is 62 heads and 38 tails. Expected value is 50 heads, 50 tails. Is the difference due to chance or a significant error? a. Draw your hypothesis
how can I win
what is difference between the blocking and confounding