STAT 121 Exam 2 review
T or F Increasing the sample size will lead to a wider margin of error.
False
The value of a sample statistic usually equals the value of the parameter of the population from which the sample was taken. t or f
False
2 signs the control chart is OUT OF CONTROL?
1. one point is way above or below the lower or upper limit 2. run of 9 points in a row on the same line below or above the mean (centerline)
the three types of Types of Statistical Inference
1. point estimation 2. interval 3. Hypothesis
four steps for Test of significance
1. state (specific claims about parameters of interest) 2. Plan (choose procedure (estimator), specify Null hypothesis, Alternative Hypothesis, and alpha (level of significance) 3. Solve (check conditions, calculate test statistic, and figure out p-value ) 4. conclude: (compare p-value to alpha, interpret test results)
What is the lower limit of the control chart for this process?
14.4 mu - 3(sigma divided by sqrt of n)
To construct an x̄-chart for this process, what number should be used as the center line?
15.0
What is the upper limit of the control chart for this process?
15.6 mu + 3(sigma divided by sqrt of n)
What is the symbol for the population standard deviation? 1.M 2.σ 3.s 4.p
2
What is the parameter of interest? 1.the mean weight of four bags of cookies produced by this manufacturing process 2. the mean weight of all bags of cookies produced by this manufacturing process 3.the weight of a bag of cookies produced by this manufacturing process 4. all bags of cookies produced by this manufacturing process
2. the mean weight of all bags of cookies produced by this manufacturing process
Point estimation is a form of statistical inference in which, based on the sample data, we estimate the unknown parameter of interest using a range of plausible values. true or false
F
When the value of the population standard deviation is unknown, the only change that occurs in the calculation of our confidence interval is we use s rather than σ. T or F
F; you use t* instead of z* as well
x bar equals 50.15 amd mu is 50; graphically, what represents the p-value?
the area under the sampling distribution cure that is to the R of 50.15
A recent study claimed that half of all college students "drink to get drunk" at least once in a while. Believing that the true proportion is much lower, the College Alcohol Study interviews an SRS of 14,941 college students about their drinking habits and finds that 7,352 of them occasionally "drink to get drunk." What type of statistical inference is this?
Hypothesis Testing --whenever there is a counterclaim being made
estimator
a general statistic that estimates the parameter. For example, • the estimator of the population mean µ is the sample mean of x -mathematical test
the margin of error in a confidence interval covers only which kind of errors?
chance errors due to random sampling
Interval estimation is a form of statistical inference in which we estimate an unknown parameter using a single number that is calculated from the sample data. True False
false
the test stat t= x bar minus mu divided by s over the square root of n measures
how many standard errors the observed x bar is from the claimed parameter value H0
Use this scenario to answer the next three questions. One of your professors claims 90% of BYU students are currently enrolled in a religion course. To test this claim, you randomly sample 300 BYU students and find that only 78% of them are enrolled in a religion course. Based on these sample results, you have evidence against your professor's claim.
hypothesis testing
A study of child preferences for milk chocolate was performed. Based on sample results, researchers were 95% confident that the proportion of children that liked milk chocolate was between 0.75 and 0.93. What type of inference is being used? Impossible to tell based on the information provided Interval estimation Point estimation Hypothesis testing
interval estimation
The mean of the theoretical sampling distribution of x̄ gets closer to μ as n increases. T or F
is already mu
Suppose we have a very right skewed population distribution where μ = 80 and σ = 20. For random samples of size n = 100, what is the standard deviation of the sampling distribution of x-bar?
sigma divided by the square root of n ; it will always be less than the SD of population
Sampling Distribution of X bar's spread?
sigma over sq root of n
Consider this formula for a confidence interval when σ is unknown: Consider this formula for a confidence interval when σ is unknown: x bar +/- t * s/square root of n Which part of this formula is the standard error of x-bar?
standard error = s/square rt of n it also represents standard deviation of the sampling distribution of x-bar
how is the level of confidence determined?
subjectively determined by the researcher
Which one of the following is the correct representation of the margin of error when sigma is unknown?
t* s/sq rt of n
What do we use to estimate μ?
x-bar
When we decrease our sample size and maintain our level of confidence, our margin of error becomes
wider
what do we obtain from the sampling distribution of x bar in order to perform a test hypothesis?
P value
Use this information to answer the next 3 questions. The IQ level of students at a particular university has an unknown mean. A simple random sample of 100 students is found to have a sample mean IQ of x̄ = 115 and a sample standard deviation of s = 15. Calculate a 95% confidence interval for the mean IQ level of all students in this university. 1.(100, 130) 2.(112, 118) 3. (114.7, 115.3) 4. (113, 117)
(112,118)
margin of error
(Likely) maximum difference between statistic and parameter at stated confidence . everything behind the t/- sign 1. The margin of error (m) controls the width of the interval. 2. As sample size increases, m and width decrease. 3. As confidence increases, m and width increase.
The sampling distribution of x-bar gives _______ from all possible samples of the same size from the same population. 1. All values of μ 2. The single value of μ 3.All x-bar values 4. All sample values
3. all x-bar values
According to the Central Limit Theorem, for random samples, what is the approximate shape of the sampling distribution of x-bar when the population distribution is non-Normal? 1.Always Normal, even if the sample size is small 2.Always the same as the shape of the population 3. Approximately Normal if the sample size is large
3. approximately normal of the sample size is large
Suppose we have a very right skewed population distribution where μ = 80 and σ = 20. For random samples of size n = 100, what is the mean of the sampling distribution of x-bar? 1. Greater than 80 2.Less than 80 3. Equal to 80
3. equal to 80
For small random samples from a Normal population distribution, the shape of the sampling distribution of x-bar is 1. abnormal 2.uniform or flat 3. normal
3. normal
f the researcher wanted to have 95% confidence in the results with a margin of error of 5.1, how many students must be sampled? (Assume \sigma σ =15) 6 12 34 72
34; use the n= (z* x sigma divided by margin of error) squred
The sample mean, ________, is used to estimate the population mean, _________. 1.s, σ 2.p-hat, p 3.μ, x̄ 4. x̄, μ
4
Based on sample results, we are 90% confident that the mean travel time to work for workers 16 and older is between 16.8 and 25.4 minutes. What type of inference is this? Point estimation Interval estimation Hypothesis testing
Interval estimation
which one of these statements is a parameter ? 1. the standard deviation of the weights of a sample of National League Football players 2. The proportion of voters in a national sample of 1500 who say they will vote for the incumbent president 3. The median income of a sample of 300 university professors 4. The mean GPA of all incoming freshmen at a state university
Number 4; the mean GPA of ALL incoming freshman -why? parameters include Mean and All; all individuals in the POPULATION
Based on sample results, researchers estimate that μ, the mean height of all female students in a university, is 64 inches. What type of inference is being used?
Point estimation
What is the parameter of interest that the administrator wants to estimate?
The mean level of nitrogen oxide of all cars of a particular model in the very large fleet.
A statistic varies because each random sample yields a different value for the statistic. T or F
T
Increasing the confidence level will lead to a wider margin of error. True False
T
The shape of the histogram of the sample data gets closer to the shape of the normal distribution as the sample size increases
T
The standard deviation of x bar decreases as N increases
T
probabilities on individuals can only be computed using the standard normal table if the population is normally distributed T or F
T
the standard deviation of x bar is always less than the standard deviation of the pop T or F
T
What is the advantage of reporting the average of several measurements ( sampling distribution of x bar) rather than the result of a single measurement? 1.Taking several measurements makes the standard deviation larger than that of single measurement. 2. The average of several measurements will always be equal to the true mean. 3. The average of several measurements is more likely to be close to the true mean than the result of a single measurement.
The average of several measurements is more likely to be close to the true mean than the result of a single measurement.
What is the parameter the researchers are trying to estimate?
The mean number of hours each week all teenagers spend watching television
Suppose the correct answer is 56 sharks (it isn't), but the researcher can only afford to sample 25 sharks. If he wishes to maintain a 99% confidence level, what effect will this have on the resulting confidence interval?
The margin of error will be larger, resulting in a wider interval.
What statistic is used to estimate the parameter of interest?
The mean level of nitrogen oxide of a sample of cars of a particular model in the very large fleet.
What is the statistic you are using to estimate the parameter of interest? The mean number of hours each week teenagers in their sample spent watching television The proportion of time each week teenagers in their sample spent watching television The mean number of hours each week all teenagers spend watching television The proportion of time each week all teenagers spend watching television
The mean number of hours each week teenagers in their sample spent watching television Remember: statistic is just a sample value
margin of error for 99 percent confidence tells us
The most a stat differs from the parameter for the middle 99 percent of all possible stat values
What is the statistic you are using to estimate the parameter of interest? 1.The mean number of all BYU students currently enrolled in a religion course 2.The proportion of all BYU students currently enrolled in a religion course 3.The mean number of BYU students in your sample currently enrolled in a religion course 4.The proportion of BYU students in your sample currently enrolled in a religion course
The proportion of BYU students in your sample currently enrolled in a religion course with hypothesis testing we use proportion?
What is the parameter of interest? The mean number of all BYU students currently enrolled in a religion course The proportion of all BYU students currently enrolled in a religion course The mean number of BYU students in your sample currently enrolled in a religion course The proportion of BYU students in your sample currently enrolled in a religion course
The proportion of all BYU students currently enrolled in a religion course
what is the purpose of a confidence interval?
To estimate the value of a parameter
Suppose we take all possible samples of the same size from a population and for each sample, we compute x-bar. The mean of these x-bar values will be exactly equal to the mean of the population (μ) from which the samples were taken. True or False?
True
Suppose we take all possible samples of the same size from a population and for each, we compute x-bar. The standard deviation of these x-bar values will be less than or equal to the standard deviation of the population from which the samples were taken. True or False?
True
The weekly oral dosage of anabolic steroids was measured on a sample of 20 body builders. A 95% confidence interval estimate for the average weekly oral dose of anabolic steroids obtained from these results was 152 mg to 194 mg. Which of the following is a correct interpretation of 95% confidence?
Using the same procedure as was used to obtain the computed interval in repeated sampling, we will obtain intervals that contain the average weekly oral dose of anabolic steroids 95 percent of the time
statistic
a number computed from the sample mean; used to estimate the value of the parameter
which one of the statements is false about m? a a small margin of error says that we have pinned down the parameter quite precisely b for a fixed level of confidence, increasing the sample size n, reduces the m c. for a fixed sample size, decreasing the level of confidence increases the m d.to obtain a smaller m without increasing sample size, you must be willing to accept lower level of confidence
c; decreasing the level of confidence decreases m
Suppose a sample of size 250 was taken instead of size 100. How will the margin of error change? the margin of error will increase in size the margin of error will not change in size the margin of error will decrease in size
margin of error will decrease
what is a control chart?
mu + 3(sigma/ sq root of n) = upper limit mu -3(sigma/ sq root of n ) = lower limits a way to measure the input and output of a process that has variation ( could be natural or unnatural)
the null hypothesis is a statement of
no effect or change in pop parameter; researchers want to disprove this
what does significance mean ?
not likely to happen by chance if H0 is true
Use this scenario to answer the next three questions. Researchers want to estimate the amount of time teenagers spend watching television during one week. A random sample of 500 teenagers yielded a sample mean of 12.60 hours of television per week. what type of statistical inference testing is this?
point estimate
which one of the following is NOT part of the definition for p-value? probability that the null is true probability of obtaining a value of the stat the value of the stat is farther from the claimed parameter value than the observed stat the null hypothesis is assumed to be true
probability that the null is true
Whenever performing a one sample t procedure on means, we should check for
randomization and no outliers ;
standard error of x-bar
s over sq rt of n
what hypothesis does the researcher generally want to prove?
the alternative
sample results are said to be statistically significant when
the difference between the observed stat and claimed parameter given in H0 is too large to be due to chance the probability of obtaining a sample sat as extreme or more extreme than actually observed if H0 is true is too small for us to believe that H0 is correct.
standard error of x bar refers to
the estimate of the standard deviation of the sampling distribution of x bar
A test of significance is intended to assess
the evidence against the null in favor of the Ha
what two things do we need in order to compute the margin or error for a one-sample t confidence interval for mu?
the level of confidence and the standard error
the level of confidence is
the percentage of time that the procedure will produce intervals that contain the parameter value
the t-distribution with 8 degrees of freedom has ____ the standard normal distribution does
the same center but more spread; spread in t distributions have slightly less area near the center and more area and spread in their tails; therefore, t-distributions have a larger spread than normal distributions the larger the n, the larger the df and the closer the graph is to a normal table less degree of freedom, more distribution
the CLT says that
the sampling distribution of x bar is approximately normal when the sample size is large
estimate
the specific value of the estimate: x bar = 35
the standard deviation of x bar measures
the variability of the sample mean about the parameter, mu
Statistical inference can be defined as making generalizations about the population based on sample data.
true
How many tiger sharks must he sample?
use n = (z* x sigma divided by margin of error) squared
which one of the following does NOT affect m for one sample t confidence interval for mu? level of confidence sample size standard error value of the paramater mu
value of the paramater mu
