ECON 261
the confidence coefficient equals
1 - a
a 95% confidence interval for the population mean is constructed as 6+- 2 . what is the margin of error?
2
a 95% confidence interval for the population mean is constructed as 6 +- 2. what is the point estimate ?
6
what is the confidence level if a =.10?
90%
variance Variance The average of the squared differences from the mean; a common measure of dispersion. of X⎯⎯⎯ is equal to
Var(X)=σ^2/n
suppose you are constructing a confidence interval for the population mean. for a given confidence level and sample size, the width of the interval is wider for a
a larger standard deviation
for 99% confidence interval , a =
a= 1-0.99= .01
for a given sample size n, a can only be reduced
at the expense of increasing b
alpha is often referred to as the
level of significance
the two main components of a confidence interval are the
point estimate and the margin of error
the parameter p represents the _______
population proportion
statistic
random variable
suppose the competing hypotheses for a test are H: u ≤ 33 versus H : u less than 33. if the p-value for the hypothesis test is .027 and the chosen level of significance is 0.05, then the correct conclusion is
reject H and conclude that the population mean is greater than 33 at the 5% significance level
in inferential statistics, we use ______ information to make inferences about an unknown ________ parameter.
sample, population
The probability distribution of the sample mean is commonly referred to as the
sampling distribution of x with a line over the top
suppose you are constructing a confidence interval for the populatino mean. For a given confidence level and standard deviation, the width of the interval is wider for
smaller samples size
What kind of sampling is more likely to be used by political pollsters who want to ensure that each religious group is represented in the sample
stratified random sampling
what does the model y = b + b x + e tell us about the relatinoship between the variable x and y ?
x and y are linearly related, but the relationship is inexact, or stochastic
when performing a hypothesis test on u when o is known, H can never be rejected if
z ≥ 0 for a left - tailed test
For the hypothesis test of μ when o is known, the value of the test statistic is calculated as
z= X (line on top) - μ / o/square root of n
the two pieces of information that are necessary to determine the value of t are...
"the level of significance" AND "the sample size or degrees of freedom"
In hypothesis testing, two incorrect decisions are possible:
- Not rejecting the null hypothesis when it is false. - Rejecting the null hypothesis when it is true.
Suppose that the sample regression equation is y= 10 + 2x - 3x then theregression residual when x=4, x = 1 and y = 12 is
-3
A random sample of 80 observations results in 50 successes. The point estimate of the population proportion of successes is _____
.625
if a equals 0.05, then the confidence coefficient equals
.95
true of false : A 95% confidence interval for U implies that if numerous samples are taken from a population , 95% of the intervals will contain u
True
The significance level is the probability of making
a Type I error allowed probability of making a type 1 error as a: we refer to 100% as the significance level
suppose that the slope parameter in a simple linear regression model is b = -5.12 . what does this suggest about the nature of the relationship between x and y ?
negative linear relationship
A two-tailed test of the population mean is conducted at α = 0.10. The calculated test statistic is z=1.55 and P(Z> or = 1.55)=0.0606. The null hypothesis should _____.
not be rejected since the p-value = 0.1212>0.10. since this is a two tailed test the p-value is 2 x 0.0606= 0.1212 > 0.10 = a , we do not reject the null hypothesis
when testing u and o is known, H can never be rejected if Z ≤ 0 for
right-tailed test
if the population standard deviation is unknown, it can be estimated by using
s
in evaluating a regression model, why is a scatterplot a useful tool?
the scatterplot can be used to assess the linearity of the relationship.
the following characteristics describe both the z and t df distributions
the tdf distribution is bell-shaped and symmetric around 0 with asymptotic tails (the tails get closer and closer to the horizontal axis but never touch it)
True or false: The optimal values of Type I and Type II errors require a compromise in balancing the costs of each type of error.
true
the expected value of the sample mean
u
which of the following is an example of a population parameter
u
cluster sampling works best
when most of the variation in a population is within groups and not between groups
If a 95% confidence interval for the mean value of a store's customer accounts is computed as $850 + or - 70, then the null hypothesis of a two-tailed hypothesis test would be rejected if the value of u0 is less than$ _____ or greater than $ _____.
$780, $920
The two equivalent methods to solve a hypothesis test are the
- p-value approach - critical value approach
a confidence interval narrows if the following is accomplished
-the chosen confidence level decreases -the sample size increases
assume p= .40 in a sample size of n = 100. in addition, Z .025 = 1.96 and t 0.025,99=1.984. a 95% confidence interval for the population proportion is
.40 +/- 1.96 * √.40(1-.40)/100
A company decided to test the hypothesis that the average time a company's employees are spending to check their private e-mails at work is more than 6 minutes. A random sample of 40 employees were selected and they averaged 6.6 minutes. It is believed that the population standard deviation is 1.7 minutes. The α is set to 0.05. The p-value for this hypothesis test would be ______.
p value = 0.0128
Left- tailed test
p-value = P Z ≤ z bell shape is shaded on the left
right tailed test
p-value = P Z ≥ z bell curve is shaded on the right side
we use a sample statistic to make inferences about an unknown population
parameter
estimate
particular value of an estimator
what is the most typical form of a calculated confidence interval?
point estimate +- margin of error
In a hypothesis test, u0 and p0 are hypothesized values of the _____ mean and the _____ proportion, respectively.
population, population
which of the following is a descriptive measure for a qualitative variable?
proportion
When testing u and o is known, H0 can never be rejected if z< or = 0 for a
right-tailed test
Given that we are sampling from a normal population, a 100(1-a)% confidence interval for the population mean when the population standard deviation is not known is a calculated as:
x⎯± tα/2,df s/√n
when a sample statistic is used to make inferences about a population parameter, it is referred to as a/an
estimator
if the sample regression equation is y=15- 5x , which of the following is the correct interpretation of the estimated slope coefficient ?
for every unit increase in x , y decreases, on average , by 5 units
The sample size required to approximate the normal distribution depends on
how much the population varies from normality.
When testing u, the p-value is the probability of obtaining a sample mean at least as large or at least as small as the one derived from a given sample, assuming the _____ hypothesis is true.
null
We do not reject the null hypothesis when the p-value is
> or = α
A local bottler in Hawaii wishes to ensure that an average of 16 ounces of passion fruit juice is used to fill each bottle. In order to analyze the accuracy of the bottling process, he takes a random sample of 72 bottles. The mean weight of the passion fruit juice in the sample is 15.81 ounces. Assume that the population standard deviation is 1.31 ounce.
H0: μ = 16; HA: μ ≠ 16 test statistic = -1.23 find the p-value= p-value greathan equal)>0.10. What is the conclusion at α = 0.05? Do not reject H0 since the p-value is greater than the significance level. Make a recommendation to the bottler. not compromised
A quality control officer believes that the average time of use for AAA batteries differs from the claimed 8.5 hours. The QC officer takes a random sample of 30 AAA batteries and finds that the sample mean is 8.7 hours. State the null and alternative hypothesis for testing the officer's claim.
H0:u=8.5 and HA:u does not =8.5
It is advertised that the average braking distance for a small car traveling at 75 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 38 small cars at 75 miles per hour and records the braking distance. The sample average braking distance is computed as 112 feet. Assume that the population standard deviation is 20 feet.
State the null and the alternative hypotheses for the test. multiple choice 1H0: μ = 120; HA: μ ≠ 120 Calculate the value of the test statistic and the p-value.Test statistic-2.47 0.01 p-value < 0.025 Use α = 0.10 to determine if the average breaking distance differs from 120 feet. - significantly different
According to a report in USAToday, more and more parents are helping their young adult children get homes. Suppose eight persons in a random sample of 40 young adults who recently purchased a home in Kentucky received help from their parents. You have been asked to construct a 95% confidence interval for the population proportion of all young adults in Kentucky who received help from their parents. What is the margin of error for a 95% confidence interval for the population proportion?
margin of error = 1.96 (0.0632
when performing a hypothersis test on u when the value of o is unkown, the test statistic is computer as T=x*-u/s/SqRtn
t distribution with (n-1) degrees of freedom
the probability of error a fora 90% confidence interval is ______ and the probability of error a for a 99% confidence interval is _____
0.10 , .01
find the probability P(Z > 0.46) for a standard normal random variable z
0.3228
if alpha (a) equals 0.01 then the confidence coefficient equals
0.99
given the sample regression equation y =15 + 3x , the value of the residual at the point (x,y) = (1,19) is
1
AAA bateries are advertised to have a life of about 9 hours of use. with a certain level of confience, it is advertised that the life is between 8-10 hours. if 9 hours is the point estimate then the margin of error is
1 hour
Put the following steps in the p-value approach to hypothesis testing in the correct order.
1. Specify the null and alternative hypotheses. 2. Specify the significance level. 3.Calculate the value of the test statistic and its p-value. 4. State the conclusion and interpret results.
steps when formulating the competing hypotheses
1. identify the relevant population parameter of interest. 2. determine whether it is a one- or two tailed test 3. include some form of the equality sign in the null hypothesis and use the alternative hypothesis to establish a claim
The ages of MBA students at a university are normally distributed with a known population variance of 10.24. Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. What is the margin of error for a 95% confidence interval for the population mean?
1.96(3.20/6)
Consider the following hypotheses: H0: μ ≤ 62.2HA: μ > 62.2 A sample of 44 observations yields a sample mean of 63.3. Assume that the sample is drawn from a normal population with a population standard deviation of 5.1. (You may find it useful to reference the appropriate table: z table or t table)
: https://www.chegg.com/homework-help/questions-and-answers/consider-following-hypotheses-h0-622-ha-622-sample-44-observations-yields-sample-mean-633--q12241149 Find the p-value: 0.05 p-value < 0.10 What is the conclusion if α = 0.01? Do not reject H0 since the p-value is greater than α. Interpret the results at α = 0.01. We cannot conclude that the population mean is greater than 62.2 Calculate the p-value if the above sample mean was based on a sample of 116 observations:0.01 p-value < 0.025 What is the conclusion if α = 0.01?- Do not reject H0 since the p-value is greater than α. . Interpret the results at α = 0.01- We cannot conclude that the population mean is greater than 62.2.
The estimator X follows a normal distribution when the underlying population follows a ________ distribution
Normal
the basic principle of hypothesis testing is to first assume that the ___ hypothesis is true and then determine if the sample data ____ this assumption
Null, Contradicts
A Type I error occurs when we
Reject the null hypothesis when it is actually true.
At an academically challenging high school, the average GPA of a high school senior is known to be normally distributed with a variance of 0.25. A sample of 20 seniors is taken and their average GPA is found to be 2.71. Develop a 90% confidence interval for the population mean GPA.
Since , the population variance is known. Therefore , use normal distribution. Now , ; From Z-table Therefore , the 90% confidence interval for the population mean GPA is ,
Consider a population with a known standard deviation of 16.8. In order to compute an interval estimate for the population mean, a sample of 51 observations is drawn.
Solution : Given that, a ) Yes, the condition that is normally distribution, b ) = 16.8 n = 51 At 95% confidence level the z is , = 1 - 95% = 1 - 0.95 = 0.05 / 2 = 0.05 / 2 = 0.025 Z/2 = Z0.025 = 1.960 Margin of error = E = Z/2* (/n) = 1.960 * (16.8 / 51) = 4.61 Margin of error = E = 4.61 C ) n = 251 n = 51 At 95% confidence level the z is , = 1 - 95% = 1 - 0.95 = 0.05 / 2 = 0.05 / 2 = 0.025 Z/2 = Z0.025 = 1.960 Margin of error = E = Z/2* (/n) = 1.960 * (16.8 / 205) = 2.30 Margin of error = E = 2.30 d ) A wider margin of error is wider confidence inerval. 95% confidence with n = 51 Answer is correct.
If repeated samples of size n are taken from a normal population with an unknown variance, then the statistic _____ follows the t distribution with n-1 degrees of freedom.
T=x*-u/s/SqRtn
if a sample statistic consistently over- or under-estimates a population parameter, then there is
bias
Which one of the following is NOT a step we use when formulating the null and alternative hypotheses
calculate the value of the sample statistic
in practice, we use a stochastic model over a deterministic model because
certain variables that impact the response variable are not included in the model
parameter
constant
Each t distribution is identified by its
degrees of freedom
An environmental group at a local college is conducting independent tests to determine the distance a particular make of automobile will travel while consuming only 1 gallon of gas. They test a sample of five cars and obtain a mean of 28.2 miles and a standard deviation is 2.7 miles. Find the 95 percent confidence interval for the mean distance traveled by all such cars using 1 gallon of gas.
not enough information given
suppose you are constructing a confidence interval for the mean length of life of AAA bateries. you ahve the following data X (line on top)=250, n=25, alpha =.5, and z a/2=z.025=1.96. the margin of error for a 95% confience interval is closest to
.2 1.96 * .5 square root 25= .196
A 95% confidence interval for the population proportion is calculated as (0.40, 0.80) The point estimate for this interval is _____.60
.60
a certain type of light bulb is advertised to have a life of about 100 hours of use. with a certain level of confidence , it is advertised that the life is between 90 and 110 hours. if 100 hours is the point estimate, then the margin of error is
10 hours
What is the value of z fora 99% confidence interval for the population mean?
2.576 z (0.01/2
A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. Her realtor friend informs them that the last 18 houses that sold in their neighborhood took an average time of 190 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 30 days.
Ans a) Assume that the population has normal distribution. Explanation: To find confidence interval population must be symmetric ------------------ Ans b) Sample size n = 21 Sample mean = 120 Population sd = 25 Significance level = 1-99/100 = 0.01 z-critical value at 99% confidence is Confidence interval:
Specify the competing hypotheses that would be used in order to determine whether the population mean differs from 15.
H0: u=15 versus HA: u does not = 15
Specify the competing hypotheses that would be used in order to determine wherher the population mean is less than 150
H: u less than equal to 150 and H : u < 150
The mortgage foreclosure crisis that preceded the Great Recession impacted the U.S. economy in many ways, but it also impacted the foreclosure process itself as community activists better learned how to delay foreclosure, and lenders became more wary of filing faulty documentation. Suppose the duration of the eight most recent foreclosures filed in the city of Boston (from the beginning of foreclosure proceedings to the filing of the foreclosure deed, transferring the property) has been 230 days, 420 days, 340 days, 367 days, 295 days, 314 days, 385 days, and 311 days. Assume the duration is normally distributed. Construct a 99% confidence interval for the mean duration of the foreclosure process in Boston.
Solution: We are given a data of sample size n=8. 230 days, 420 days, 340 days, 367 days, 295 days, 314 days, 385 days, and 311 days Using this, first we find sample mean() and sample standard deviation(s). = = = = 332.75 Now , s= Using given data, find Xi- for each term.take squre for each.then we can easily find s. s= 59.01029 Confidence interval for population mean() using t distribution Given that, = 332.75 ....... Sample mean s = 59.01029 ........Sample standard deviation n = 8 ....... Sample size Note that, Population standard deviation() is unknown..So we use t distribution. Our aim is to construct 99% confidence interval. c = 0.99 = 1- c = 1- 0.99 = 0.01 /2 = 0.01 2 = 0.005 Also, n = 8 d.f= n-1 = 7 = = = 3.499 ( use t table or t calculator to find this value..) Now , confidence interval for mean() is given by: 332.75 - 3.499*(59.01029/ 8) 332.75 + 3.499*(59.01029/ 8) 259.7393 < < 405.7607 is the required 95% confidence interval for mean....
The four step procedure using the p-value approach
Step 1. Specify the null and the alternative hypotheses. We identify the relevant population parameter of interest, determine whether it is a one- or a two-tailed test and, most importantly, include some form of the equality sign in the null hypothesis and place whatever we wish to establish in the alternative hypothesis. Step 2. Specify the significance level. Before implementing a hypothesis test, we first specify α, which is the allowed probability of making a Type I error. Step 3. Calculate the value of the test statistic and the p-value. When the population standard deviation σ is known, the value of the test statistic is z=x⎯⎯−μσ/n‾√, where μ0 is the hypothesized value of the population mean. For a right-tailed test, the p-value isP(Z≥z), and for a left-tailed test, the p-value is P(Z≤z). For a two-tailed test, the p-value is 2P(Z≥z) if z>0, or2P(Z≤z) if z<0. Step 4. State the conclusion and interpret results. The decision rule is to reject the null hypothesis when the p-value<α and not reject the null hypothesis when the p-value≥α. Clearly interpret the results in the context of a problem.
if repeated samples of size n are taken from a normal population with an unknown variance, then the statistic ____ follows the t distribution with n-1 degrees of freedom
T= x-u / (s/√n)
The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor's degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The α is set to 0.05. The p-value for this hypothesis test would be ______
Test Hypothesis:H0 : μ = $17000H1 : μ ≠ $17000 Test Statistic:Z = x̅ - μ/(σ/√n)= 18200- 17000/(4200/√34)= 1.67 P-value = 0.0949 P-value = 0.0949 in this context is greater than 0.05, so the null hypothesis is not rejected at 5% level of significance.There is insufficient evidence to indicate that the average debt load of graduating students with a Bachelor's degree is not equal to $17,000. The result is not statistically significant. The option is D.Because the p-value is greater than α, we fail to reject the null hypothesis and cannot conclude that the average debt load is not equal to $17,000.
Using data from 50 workers, a researcher estimates Wage = β0 + β1Education + β2Experience + β3Age + ε, where Wage is the hourly wage rate and Education, Experience, and Age are the years of higher education, the years of experience, and the age of the worker, respectively. The regression results are shown in the following table. CoefficientsStandardErrort Statp-ValueIntercept7.053.591.960.0556Education1.690.305.630.0000Experience0.380.132.920.0054Age−0.060.08−0.750.4571
The regression equation is given as y=7.05+1.69*Education+0.38*Experience-0.06*Age Predicted hourly wage rate =7.05+1.69*1 (please use correct value of higher education from dataset) + 0.38*2-0.06*23 Please feel free to resolve this in comments if more help is required. thanks Interpret the point estimate for β1. As Education increases by 1 year, Wage is predicted to increase by 1.69/hour, holding Age and Experience constant. . Interpret the point estimate for β2. As Experience increases by 1 year, Wage is predicted to increase by 0.38/hour, holding Age and Education constant. Predict the hourly wage rate for a 23-year-old worker with 4 years of higher education and 2 years of experience. = 7/05 + 1.69 (4) + /38 (2)-.06(23)= 13.19
Consider the following sample regression equation: y= 17 - 3x = 3x what will be the average change in the estimated value of y , given a unit chaine in x (holding x constant)
decrease by 3 units
in regression analysis, the response variable is also called the
dependent variable
Whenever we construct a confidence interval for the population mean , the margin of error includes the standard error of X (line on top) and the
desired level of confidence
the multiple regression model used when?
examine how the response variable is influenced by two or more explanatory variables. - the reasercher believes that two or more explanatory variables influence the response variable
if x is normally distributed with expected value and standard deviation then normally distributed with
expected value u and standard deviation σ/√n
A 95% confidence interval for the population mean is calculated as (40,80) . the margin of error for this interval is 20
first find the point estimate (40+80)/2= 60. then margin of error can be found as 80-60= 20 or 60-40=20
if the sample regression equation is y=15 + 5x, which of the following is the correct interpretation of 5?
for every unit increase in x , y increases , on average , by 5 units.
If the sample regression equation is yhat=15+5x, which of the following is the correct interpretation of 15?
for every unit increase in x, y ^ increases, on average, by 5 units
a 95% confidence interval for the population mean implies that
for repeated samples, 95% of the sample means will fall within the interval
Consider the following hypotheses: H0: μ ≥ 185 HA: μ < 185 The population is normally distributed. A sample produces the following observations: 170 162 181 182 172 167 Use the critical value approach to conduct the test at a 1% level of significance. Use Table 2. a. Find the mean and the standard deviation. (Round intermediate calculations to 4 d
https://www.chegg.com/homework-help/questions-and-answers/consider-following-hypotheses-h0-185-ha-185-population-normally-distributed-sample-produce-q13605179
we can generally reduce both type 1 and type 2 errors simultaneously by
increasing the sample size
in regression analysis , the explanatory variable is also called the
independent variable
The branch of statistics that uses sample statistics to estimate a population parameter or test a hypothesis about such a parameter is BEST referred to as
inferential statistics
what is a primary requirement of a "good"' sample?
it is representative of the population we are trying to describe
a sample statistic is considered biased it
it systematically over- or under-estimates the unknown parameter being estimated
the allowed probability that an interval estimate of a population mean will not contain u is referred to as the
level of significance
the common approach to fitting a line to a sample data in a scatterplot is to
minimize the value of the sum of the squared residuals.
in order to construct interval for u , the sampling distribution of the estimter X line on top must follow or approx. follow a(n) ______ distribution
normal
when the sample size is sufficiently large , we can approximate the sampling distribution of the sample proportion using the _____ distribution
normal
The two competing hypotheses used in hypothesis testing are called the _____ hypothesis and the _____ hypothesis.
null, alternative
Alternative hypothesis 1. H: u > u 2. H : u<u 3. H : u does not = U
p value 1- Right-tail probability: P(Z≥z) 2- Left-tail probability: P(Z≤z) 3 - Two-tail probability: 2P(Z≥z) if z>0 or 2P(Z≤z) if z<0
The mean and standard deviation are often used to describe ____ data while the proportion is a descriptive measure that can also be used for ____ date
quantitative, qualitative
a confidence interval can be interpreted as a
range of values used to estimate and unknown population parameter
standard error sample mean, computed as
se(X)= σ/√n
We use the t distribution to construct a confidence interval for the population mean when the underlying population standard deviation is not known. Under the assumption that the population is normally distributed, find tα/2,df for the following scenarios.
solution given that (A)n = 25 Degrees of freedom = df = n - 1 = 25- 1 = 24 At 90% confidence level the t is , = 1 - 90% = 1 - 0.90 = 0.1 / 2 = 0.1 / 2 = 0.05 t /2,df = t0.05,24 = 1.711 ( using student t table) (B) n = 25 Degrees of freedom = df = n - 1 = 25- 1 = 24 At 95% confidence level the t is , = 1 - 95% = 1 - 0.95 = 0.05 / 2= 0.05 / 2 = 0.025 t /2,df = t0.025,24 = 2.064 ( using student t table)
An important final conclusion to statistical test is to
Clearly interpret the results in terms of the initial claim
A Type II error occurs when we
Do not reject the null hypothesis when it is actually false.
Specify the competing hypotheses that would be used in order to determine whether the population mean differs from 0.60
H0: u=0.60 versus HA: u does not = .60
A 95% confidence interval for the population mean is calculated as (40,80). The point estimate for this interval is 60
The point estimate is calculated as (40 + 80)/2= 60
What is the characteristic of a "bad" sample
The sample is not representative of the population we are trying to describe
A left-tailed test of the population mean is conducted at α = 0.10. The calculated test statistic is z=1.55 and P(Z> or = 1.55)=0.0606. The null hypothesis should _____.
be rejected since the p-value = 0.0606< 0.10
The central limit theorem states that, for any distribution, as n gets larger, the sampling distribution of the sample mean becomes-
closer to a normal distribution
it is advertised that the average braking distance for a small car traveling at 75 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 38 small cars at 75 miles per hour and records the braking distance. The sample average braking distance is computed as 112 feet. Assume that the population standard deviation is 20 feet a. State the null and the alternative hypotheses for the test. A)H0: μ = 120; HA: μ ≠ 120 B)H0: μ ≥ 120; HA: μ < 120 C)H0: μ ≤ 120; HA: μ > 120 b. Calculate the value of the test statistic and the p-value. Find the p-value. A)0.025 p-value < 0.05 B) 0.05 p-value < 0.10 C)p-value 0.10 D)p-value < 0.01 E)0.01 p-value < 0.025 Use α = 0.10 to determine if the average breaking distance differs from 120 feet.
https://www.chegg.com/homework-help/questions-and-answers/advertised-average-braking-distance-small-car-traveling-75-miles-per-hour-equals-120-feet--q49931831?trackid=c28d35308e20&strackid=eed9e4b1986f
a confidence interval narrows if the following is accomplished
the chossen confidence level decreases the sample size increases
When constructing a confidence interval for the population mean, the factors that affect the width of the confidence interval for a given standard deviation are
the confidence level and the sample size
Consider the following hypotheses: H0: μ ≥ 130HA: μ < 130 A sample of 74 observations results in a sample mean of 125. The population standard deviation is known to be 31. (You may find it useful to reference the appropriate table: z table or t table) a-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
test statistic = -1.3874 Find p-value = 0.05 p-value < 0.10 Does the above sample evidence enable us to reject the null hypothesis at α = 0.10 = Yes since the p-value is less than the significance level. Does the above sample evidence enable us to reject the null hypothesis at α = 0.01?=No since the p-value is greater than the significance level. Interpret the results at α = 0.01.= We cannot conclude that the population mean is less than 130
if the sample regression equation is y=15 + 5x , which of the following is the correct interpretation of the estimated intercept
the line crosses the y axis at y =15
if we were to sample repeatedly from a given population, the average value of the sample means will equal
the population mean
When estimating the population mean, the T distribution is used when the
the population variance is unknown
why is the stochastic model used in regression analysis in place of the deterministic model?
the relationship between the response andthe explanatory variables is inexact, or imperfect
for which of the following situations is the multiple regression model appropriate ?
the response variable is influenced by two or more explanatory variables.
The two pieces of information that are necessary to determine the value of t are
the sample size or degrees of freedom and the level of significance
selection bias occurs when
there is a systematic exclusion of certain groups from consideration for the sample
Stratified sampling is preferred to cluster sampling when the objective is
to increase precision
suppose you are constructing a confidence interval for the population mean . for a given sample size and standard deviation, the width of the confidence interval is ____ for a greater confidence level
wider
