Question 1
Why can you never have 100% confidence in correctly estimating the population characteristic of interest?
When are you able to use the t distribution to develop the confidence interval estimation for the mean?
Why is it true that for a given sample size, n, an increase in confidence is acheived by widening (and making less precise) the confidence interval?
Why is the sample size needed to determine the proportion smaller when the population proportion is 0.20 than when the population proportion is 0.50?
What is the difference between a null hypothesis, H0, and an alternative hypothesis, H1?
What is the difference between a one-tailed test and a two-tailed test?
What is meant by a p value?
What is the six step critical value approach to hypthesis testing? List the six steps.
Why can you never have 100% confidence in correctly estimating the population characteristic of interest?
In statistics, a confidence interval (CI) is a kind of interval
estimate of a population parameter and is used to indicate the
reliability of an estimate. It is an observed interval (i.e. it is
calculated from the observations), in principle different from
sample to sample, that frequently includes the parameter of
interest, if the experiment is repeated. How frequently the
observed interval contains the parameter is determined by the
confidence level or confidence coefficient. More specifically, the
meaning of the term "confidence level" is that, if confidence
intervals are constructed across many separate data analyses of
repeated (and possibly different) experiments, the proportion of
such intervals that contain the true value of the parameter will
match the confidence level; this is guaranteed by the reasoning
underlying the construction of confidence intervals.[1][2][3]
Confidence intervals consist of a range of values (interval) that
act as good estimates of the unknown population parameter. However,
in rare cases, none of these values may cover the value of the
parameter. The level of confidence of the confidence interval would
indicate the probability that the confidence range captures this
true population parameter given a distribution of samples. It does
not describe any single sample. This value is represented by a
percentage, so when we say, "we are 99% confident that the true
value of the parameter is in our confidence interval", we express
that 99% of the observed confidence intervals will hold the true
value of the parameter. After a sample is taken, the population
parameter is either in the interval made or not, there is no
chance. The level of confidence is set by the researcher (not
determined by data) . If a corresponding hypothesis test is
performed, the confidence level corresponds with the level of
significance, i.e. a 95% confidence interval reflects an
significance level of 0.05, and the confidence interval contains
the parameter values that, when tested, should not be rejected with
the same sample. Greater levels of confidence give larger
confidence intervals, and hence less precise estimates of the
parameter. Confidence intervals of difference parameters not
containing 0 imply that that there is a statistically significant
difference between the populations.
Certain factors may affect the confidence interval size including
size of sample, level of confidence, and population variability. A
larger sample size normally will lead to a better estimate of the
population parameter.
A confidence interval does not predict that the true value of the
parameter has a particular probability of being in the confidence
interval given the data actually obtained. (An interval intended to
have such a property, called a credible interval, can be estimated
using Bayesian methods; but such methods bring with them their own
distinct strengths and weaknesses).
When are you able to use the t distribution to develop the confidence interval estimation for the mean?
Student’s t-distribution (or simply the t-distribution) is a family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.
Why is it true that for a given sample size, n, an increase in confidence is acheived by widening (and making less precise) the confidence interval?
Why is the sample size needed to determine the proportion smaller when the population proportion is 0.20 than when the population proportion is 0.50?
The sample size formula for p is: n = (z/ME)^2 * p * (1-p)
The required sample size is the largest when p = .5, because the
quantity p * (1-p) is the largest when p = .5, i.e.
.1 * (1-.1) = .09
.3 * (1-.3) = .21
.5 * (1-.5) = .25
.7 * (1-.7) = .21
.9 * (1-.9) = .01
Question 1 Why can you never have 100% confidence in correctly estimating the population characteristic of interest? Whe...
8.50 Why can you never really have 100% confidence of correctly estimating the population characteristic of interest?
Is there a relationship between confidence intervals and two-tailed hypothesis tests? Let c be the level of confidence used to construct a confidence interval from sample data. Let α be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the mean. For a two-tailed hypothesis test with level of significance α and null hypothesis H0: μ = k, we reject H0 whenever k falls outside the c = 1 − α confidence...
A business student is interested in estimating the 95% confidence interval for the proportion of students who bring laptops to campus. He wishes a precise estimate and is willing to draw a large sample that will keep the sample proportion within six percentage points of the population proportion. What is the minimum sample size required by this student, given that no prior estimate of the population proportion is available? Use Table 1. (Round intermediate calculations to 4 decimal places and...
Question 1 to 11, True or False? Applied business statistics 1) The width of the confidence interval depends only on the desired level of confidence 2) When population standard deviation is unknown, sample standaird deviation is used and the interval estimation is based on values from the t- rather than the z-distribution n 3) The z value for a 98% confidence interval around the point estimate is 2.33 4) In order to construct a 90% confidence interval for the population...
a. You wish to compute the 95% confidence interval for the population proportion. How large a sample should you draw to ensure that the sample proportion does not deviate from the population proportion by more than 0.12? No prior estimate for the population proportion is available. Round intermediate calculations to at least 4 decimal places and "z" value to 3 decimal places. Round up your answer to the nearest whole number.) Sample Size - b. A business student is interested...
Use the confidence level and sample data to find a confidence interval for estimating the population. Round your answer to the same number of decimal places as the sample mean 19) A group of 5 randomly selected students have a mean score of 295 with a standard deviation of 19 5.2 on a placement test. What is the 90% confidence interval for the mean score of all students taking the test? A) 27.8 < <312 ) 27.9<<311 C)282 << 308...
3. True or False? a) We use the sample proportions when to check the 4th condition when doing a hypothesis test for the difference of two population proportions. b) A 100% confidence interval for the difference of two population proportions is (0, 1). c) It is possible for p> 3 to be used as your null hypothesis when doing a hypothesis test to see if a population proportion is greater than 3. d) You find a confidence interval for the...
In the picture below, I have the output for the same two sets of data. I ran the hypothesis test and the confidence interval. If you had a choice to use one output or the other, which would you choose and why? Make sure to be specific and include what information you get from each and what information you don't get if you use one over the other. Options Two sample T summary hypothesis test: : Mean of Population 1...
Suppose that you are testing the hypotheses Ho: p= 0.20 vs. HA, p 0.20. A sample of size 250 results in a sample proportion of 0.27 a) Construct a 95% confidence interval for p. b) Based on the confidence interval, can you reject Ho at a 0.05? Explain c) What is the difference between the standard error and standard deviation of the sample proportion? d) Which is used in computing the confidence interval? a) The 95% confidence interval for p...
1. When 385 junior college students were surveyed, 170 said that they have previously 1). owned a motorcycle. Find a point estimate for p. the population proportion of students who have previously owned a motorcycle. A) 0.558 B) 0.442 C) 0.306 D) 0.791 2. True or False: The general form of a large-sample (1 - a) 100% confidence interval 2) p(1-P) for a population proportion pis ptz, where p = is the sample proportion of observations with the characteristic of...