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Instructions of Test-2 (STAT-101)

The due date of Test 2 is Monday, January 30, 2023, at 11:00 PM.

Test 2 covers the material of Weeks 5, 7 & 8

The test consists of 25 questions

10T/F (0.25 marks each) and 15MCQ (0.5marks each)

Total Marks = 10

You have only one attempt.

You have a time limit of 5 hours (300 minutes).

This assignment will be saved and submitted automatically when the time (5hrs) is expired.

This assignment can be saved and resumed at any point until the time (5hrs) has expired.

The time will continue to run if you leave the test.

STAT 101_SEU 00967775703091 Assignment _2_2023 2_نموذج

Review Test Submission: Assignment2-STAT101- 2022-23-2nd

User

Course (Current Semester – الفصل الحالي)STAT-101: Statistics *******************

Test Assignment2-STAT101-2022-23-2nd

Started 1/27/23 11:52 PM

Submitted 1/28/23 1:55 AM

Due Date 1/30/23 11:00 PM

Status Completed

Attempt Score

9.75 out of 10 points

Time Elapsed

2 hours, 3 minutes out of 5 hours

Instructions Instructions of Assignment-2(STAT-101) The display date of Assignment 2 is Wednesday, January 25,

2023, 11:00 P.M. The due date of Assignment 2 is Monday, January 30, 2023, at

11:00 PM.

Assignment 2 covers the material of Weeks 5, 7, & 8 (Chapters-6,

7 & 8)

The assignment consists of 25 questions 10T/F (0.25 marks each) and 15MCQ (0.5marks each)

Total Marks = 10

You have only one attempt.

You have a time limit of 5 hours (300 minutes). This assignment will be saved and submitted automatically when

the time (5hrs) is expired. This assignment can be saved and resumed at any point until the

time (5hrs) has expired. The time will continue to run if you leave the test.

Good luck!

Saturday, January 28, 2023 1:56:01 AM AST

STAT 101_SEU 00967775703091 Assignment _2_2023 2_نموذج

Question 1

If the total area under standard normal probability distribution is k+1, then the value

of k is zero.

True

False

Question 2

If the z-score of normal distribution is –2.50, the mean of the distribution is 35 and the

standard deviation of normal distribution is 2, then the value of X for a normal

distribution is 40.

True

False

Question 3 Given that Z is a standard normal random variable. If P(Z > k)=0.0505, then the value of k is 1.64

True

False

Question 4

A confidence interval (or interval estimate) is a range (or an interval) of values used

to estimate the true value of a population parameter.

True

False

Question 5

The sample mean is not the best point estimate of the population mean.

True

False

Question 6

If the P-value for a one-sided test for testing a mean is 0.05, then the P-value for the

corresponding two-sided test would be 0.01.

True

False

Question 7

The probability of rejecting the null hypothesis when it is true is called Level of

significance.

True

False

Question 8

The alternative hypothesis for the following claim: “A car Company claims that its new car

will average more than 40 miles per gallon in the city” is H1: µ < 40.

True

False

STAT 101_SEU 00967775703091 Assignment _2_2023 2_نموذج

Question 9

The alternative hypothesis for the following claim: “A motorbike company claims that its new

model will give an average at least 60 km/l on a long route” is Ha: µ < 60.

True

False

Question 10

If the original claim says that the mean working hours in a day are same for men and

women in a company. Then symbolically it is represented as p1 = p2.

True

False

Question 11

You are given the following hypothesis test:

H0: μ=100

H1: μ ≠ 100 The calculated test statistic z = –1.0, and the critical value of z = ±1.97. Then, the

decision would be to:

Reject H0 since z < –1.97

Reject H0 since –1.97 < z < 1.97

Fail to reject H0 since –1.97 < z < 1.97

Fail to reject H0 since z < –1.97

Question 12

A prescription allergy medicine is supposed to contain an average of 245 parts per

million (ppm) of active ingredient. The manufacturer periodically collects data to

determine if the production process is working properly. A random sample of 64 pills

has a mean of 250 ppm with a standard deviation of 12 ppm.

Let µ denotes the average amount of the active ingredient in pills of this allergy

medicine. The null and alternative hypotheses are as H0: µ = 245, Ha:µ ≠ 245. The

level of significance is 1%.

The t-test statistic is 3.33 with a P-value of 0.0014. What is the correct conclusion?

The mean amount of active ingredient in pills of this allergy medicine is equal to 245

ppm.

The mean amount of active ingredient in pills of this allergy medicine is equal to 250

ppm.

The mean amount of active ingredient in pills of this allergy medicine is not equal to 245

ppm.

The mean amount of active ingredient in pills of this allergy medicine is greater than 245

ppm.

Question 13

Among 169 Egyptian-African men, the mean systolic blood pressure was 145 mmHg

with a standard deviation of 26. The t-test statistic to conclude that the mean systolic

blood pressure for a population of Egyptian-African men is greater than 142 is

-2.5

-1.3

1.5

-1.5

STAT 101_SEU 00967775703091 Assignment _2_2023 2_نموذج

Question 14

The degree of confidence is equal to:

1-α

1-β

Question 15

When carrying out a large sample test of H0: µ0 = 50, Ha: µ0 < 50, we reject H0 at

level of significance α when the calculated test statistic is:

Greater than zα

Less than – zα

Greater than zα/2

Less than zα

Question 16

A sample of 100 body temperatures has a mean of 98.6 oF. Assume that σ is known to

be 0.5 oF. Use a 0.05 significance level to test the claim that the mean body

temperature of the population is equal to 98.5 oF, as is commonly believed. What is

the value of test statistic for this testing?

1.0

3.0

-2.0

2.0

Question 17

With H0: μ = 100, Ha: μ < 100, the test statistic is z = – 1.75. Using a 0.05

significance level, the P-value and the conclusion about null hypothesis are (Given

that P(z < 1.75) =0.9599)

0.0401; reject H0

0.9599; fail to reject H0

0.0401; fail to reject H0

0.9599; reject H0

Question 18

A passing student is failed by an examiner, it is an example of:

Type-I error

Type-II error

Best Decision

All of above

Question 19

The confidence interval, 0.548 < p < 0.834 is obtained for a population proportion, p.

The margin of error, E using these confidence interval limits is

0.143

0.286

0.691

1.382

STAT 101_SEU 00967775703091 Assignment _2_2023 2_نموذج

Question 20

If the point estimate 𝑝 ̂ is 0.8 and the lower confidence limit is 0.6, then the upper

confidence limit is:

1.0

0.7

0.6

0.4

Question 21

If the Margin of error E is 0.5 and the upper confidence limit is 9, then the lower

confidence limit is:

Question 22 Evaluate P(-1< Z< 2), where P(Z < 2)=0.9772 and P(Z< -1)=0.1587

c. -0.1359

d. 0.8185

b. 0.1359

a. -0.8185

Question 23

The normal probability distribution curve is symmetrical about mean µ. Then P(X <

μ) = P(X > μ) is equal to

0.25

0.50

0.75

STAT 101_SEU 00967775703091 Assignment _2_2023 2_نموذج

Question 24 Which of the following is NOT true regarding the normal distribution?

d. The points of the curve meet the X-axis at z = –3 and z = 3

b. It has a single peak

c. It is symmetrical

a. Mean, median and mode are all equal

Question 25 Assume that the thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1°C for freezing water. If one thermometer is randomly selected, find the probability that it reads (at the freezing point of water) greater than -1.75 degrees.

a. 0.0401

b. -0.9599

c. 0.9599

d. None

Lecture Slides

Elementary Statistics Eleventh Edition

and the Triola Statistics Series

by Mario F. Triola

Chapter 7

Estimates and Sample Sizes

7-1 Review and Preview

7-2 Estimating a Population Proportion

7-3 Estimating a Population Mean: σ Known

7-4 Estimating a Population Mean: σ Not Known

7-5 Estimating a Population Variance

Section 7-1

Review and Preview

Review

❖ Chapters 2 & 3 we used “descriptive statistics” when we summarized data using tools such as graphs, and statistics such as the mean and standard deviation.

❖ Chapter 6 we introduced critical values: z denotes the z score with an area of  to its right. If  = 0.025, the critical value is z0.025 = 1.96. That is, the critical value z0.025 = 1.96 has an area of 0.025 to its right.

Preview

❖ The two major activities of inferential statistics are (1) to use sample data to estimate values of a population parameters, and (2) to test hypotheses or claims made about population parameters.

❖ We introduce methods for estimating values of these important population parameters: proportions, means, and variances.

❖ We also present methods for determining sample sizes necessary to estimate those parameters.

This chapter presents the beginning of inferential statistics.

Section 7-2

Estimating a Population

Proportion

Key Concept In this section we present methods for using a

sample proportion to estimate the value of a

population proportion.

• The sample proportion is the best point

estimate of the population proportion.

• We can use a sample proportion to construct a

confidence interval to estimate the true value

of a population proportion, and we should

know how to interpret such confidence

intervals.

• We should know how to find the sample size

necessary to estimate a population proportion.

Definition

A point estimate is a single value (or

point) used to approximate a population

parameter.

The sample proportion p is the best

point estimate of the population

proportion p.

Definition

Example:

Because the sample proportion is the best point estimate of the population proportion, we conclude that the best point estimate of p is 0.70. When using the sample results to estimate the percentage of all adults in the United States who believe in global warming, the best estimate is 70%.

In the Chapter Problem we noted that in a Pew Research Center poll, 70% of 1501 randomly selected adults in the United States believe in global warming, so the sample proportion is

= 0.70. Find the best point estimate of the proportion of all adults in the United States who believe in global warming.

p̂

Definition

A confidence interval (or interval

estimate) is a range (or an interval)

of values used to estimate the true

value of a population parameter. A

confidence interval is sometimes

abbreviated as CI.

A confidence level is the probability 1 –  (often

expressed as the equivalent percentage value)

that the confidence interval actually does contain

the population parameter, assuming that the

estimation process is repeated a large number of

times. (The confidence level is also called degree

of confidence, or the confidence coefficient.)

Most common choices are 90%, 95%, or 99%.

( = 10%), ( = 5%), ( = 1%)

Definition

We must be careful to interpret confidence intervals correctly. There is a correct interpretation and many different and creative incorrect interpretations of the confidence interval 0.677 < p < 0.723.

“We are 95% confident that the interval from 0.677 to 0.723 actually does contain the true value of the population proportion p.”

This means that if we were to select many different samples of size 1501 and construct the corresponding confidence intervals, 95% of them would actually contain the value of the population proportion p.

(Note that in this correct interpretation, the level of 95% refers to the success rate of the process being used to estimate the proportion.)

Interpreting a Confidence Interval

Know the correct interpretation of a confidence interval.

Caution

Confidence intervals can be used informally to compare different data sets, but the overlapping of confidence intervals should not be used for making formal and final conclusions about equality of proportions.

Caution

Critical Values A standard z score can be used to distinguish between sample statistics that are likely to occur and those that are unlikely to occur. Such a z score is called a critical value. Critical values are based on the following observations:

1. Under certain conditions, the sampling distribution of sample proportions can be approximated by a normal distribution.

Critical Values

2. A z score associated with a sample proportion has a probability of /2 of falling in the right tail.

Critical Values

3. The z score separating the right-tail region is

commonly denoted by z/2 and is referred to

as a critical value because it is on the

borderline separating z scores from sample

proportions that are likely to occur from those

that are unlikely to occur.

Definition

A critical value is the number on the

borderline separating sample statistics

that are likely to occur from those that are

unlikely to occur. The number z/2 is a

critical value that is a z score with the

property that it separates an area of /2 in

the right tail of the standard normal

distribution.

The Critical Value z2

Notation for Critical Value

The critical value z/2 is the positive z value

that is at the vertical boundary separating an

area of /2 in the right tail of the standard

normal distribution. (The value of –z/2 is at

the vertical boundary for the area of /2 in the

left tail.) The subscript /2 is simply a

reminder that the z score separates an area of

/2 in the right tail of the standard normal

distribution.

Finding z2 for a 95%

Confidence Level

-z2 z2

Critical Values

 2 = 2.5% = .025

 = 5%

z2 = 1.96−+

Use Table A-2 to find a z score of 1.96

 = 0.05

Finding z2 for a 95%

Confidence Level – cont

Definition

When data from a simple random sample are

used to estimate a population proportion p, the

margin of error, denoted by E, is the maximum

likely difference (with probability 1 – , such as

0.95) between the observed proportion and

the true value of the population proportion p.

The margin of error E is also called the

maximum error of the estimate and can be found

by multiplying the critical value and the standard

deviation of the sample proportions:

p̂

Margin of Error for

Proportions

ˆ ˆpq E z

n =

p = population proportion

Confidence Interval for Estimating

a Population Proportion p

= sample proportion

n = number of sample values

E = margin of error

z/2 = z score separating an area of /2 in the right tail of the standard normal distribution

p̂

Confidence Interval for Estimating

a Population Proportion p

1. The sample is a simple random sample.

2. The conditions for the binomial distribution

are satisfied: there is a fixed number of

trials, the trials are independent, there are

two categories of outcomes, and the

probabilities remain constant for each trial.

3. There are at least 5 successes and 5

failures.

Confidence Interval for Estimating

a Population Proportion p

p – E < < + Eˆ p̂p

where

ˆ ˆpq E z

n =

p – E < < + E

p + E

ppˆ ˆ

Confidence Interval for Estimating

a Population Proportion p

(p – E, p + E)ˆ ˆ

Round-Off Rule for

Confidence Interval Estimates of p

Round the confidence interval limits

for p to

three significant digits.

1. Verify that the required assumptions are satisfied.

(The sample is a simple random sample, the

conditions for the binomial distribution are satisfied,

and the normal distribution can be used to

approximate the distribution of sample proportions

because np  5, and nq  5 are both satisfied.)

2. Refer to Table A-2 and find the critical value z /2 that

corresponds to the desired confidence level.

3. Evaluate the margin of error

Procedure for Constructing

a Confidence Interval for p

2 ˆ ˆE z pq n=

4. Using the value of the calculated margin of error, E

and the value of the sample proportion, p, find the

values of p – E and p + E. Substitute those values

in the general format for the confidence interval:

ˆ ˆ ˆ

p – E < p < p + Eˆ ˆ

5. Round the resulting confidence interval limits to

three significant digits.

Procedure for Constructing

a Confidence Interval for p – cont

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