Is the sample size large enough to compute a confidence interval for the proportion of adults ages 18-34 who are dissatisfied with their job? A recent study by Pew Research randomly sampled 456 working adults ages 18-34 and asked them if they were dissatisfied with their job. Of the adults sampled, 234 said “
yes
“.
Were the data appropriately collected for performing a two sample z test on proportions?
Were the data appropriately collected for performing a two-sample z test of significance procedure on proportions?
Yes
, the subjects available for the study were randomly allocated to either the Botox treatment group or the placebo (salt water) treatment group.
What is the 95% confidence interval estimate for the percent of all adults who want to lose weight?
†Based on this poll, the 95% confidence interval for the population proportion who want to lose weight is
(0.56, 0.62)
.
How likely is it to observe a difference of 0.09 or more extreme if there is no difference in the mean GPA for male and female scholarship athletes?
How likely is it to observe a mean GPA difference of 0.09 if there is no difference in the mean GPA for male and female scholarship athletes? … If there is no difference in the mean GPA of male and female athletes, the probability of obtaining this difference (3.11 – 3.02 = 0.09) is
approximately 0.287
.
Is the sample size large enough to compute a confidence interval for the proportion of adults ages 18 34 who are dissatisfied with their job?
Is the sample size large enough to compute a confidence interval for the proportion of adults ages 18-34 who are dissatisfied with their job? A recent study by Pew Research randomly sampled 456 working adults ages 18-34 and asked them if they were dissatisfied with their job. Of the adults sampled, 234 said “
yes
“.
Which of the following would produce the widest confidence interval?
Answer and Explanation:
The Z-score value increases with the increase in confidence level and hence, we can say that the highest confidence level among the given options
(i.e.d) 99%
) will yield the widest confidence interval.
What is the advantage of a histogram over a stem plot or dot plot?
What is an advantage of a histogram over a stemplot or dotplot? a.
Histograms work well for very large data sets
. The following three histograms all display the same data set.
How would the shape of a confidence change if the sample size has decreased?
If we decrease the sample size n to 25, we
increase the error bound
. Increasing the sample size causes the error bound to decrease, making the confidence interval narrower. Decreasing the sample size causes the error bound to increase, making the confidence interval wider.
How does the shape of the confidence interval change if the confidence level increases from 90 to 95?
3) a) A 90% Confidence Interval would be
narrower
than a 95% Confidence Interval. This occurs because the as the precision of the confidence interval increases (ie CI width decreasing), the reliability of an interval containing the actual mean decreases (less of a range to possibly cover the mean).
What does this margin of error account for?
The margin of error expresses
the amount of the random variation underlying a survey’s results
. This can be thought of as a measure of the variation one would see in reported percentages if the same poll were taken multiple times.
What are the similarities and differences between conducting a hypothesis test and constructing a confidence interval?
Confidence intervals and hypothesis tests are similar in that they are
both inferential methods that rely on an approximated sampling distribution
. Confidence intervals use data from a sample to estimate a population parameter.
What is the relationship between confidence intervals and levels of significance?
You can use either P values or confidence intervals to determine whether your results are statistically significant. If a hypothesis test produces both, these results will agree. The confidence level is
equivalent to 1
– the alpha level. So, if your significance level is 0.05, the corresponding confidence level is 95%.
How do you use confidence intervals to test a hypothesis?
The key to understanding this is to realize that a
level C = (1 – α) ⋅ 100% confidence interval
gives us the same results as a hypothesis test using a level of significance α. For example, a 95% confidence interval can be used in place of a hypothesis test using a significance level α = 0.05 = 5%.
Is p-value the probability that the null hypothesis is true?
The p-value is
the probability that the null hypothesis is true
. … A low p-value shows that the effect is large or that the result is of major theoretical, clinical or practical importance. A non-significant result, leading us not to reject the null hypothesis, is evidence that the null hypothesis is true.
Is the level of significance or the probability of a Type I error?
The probability of making a type I error is
α
, which is the level of significance you set for your hypothesis test. An α of 0.05 indicates that you are willing to accept a 5% chance that you are wrong when you reject the null hypothesis.
When our p-value is less than our level of significance α What can we conclude?
Using P values and Significance Levels Together
If your P value is less than or equal to your alpha level,
reject the null hypothesis
. The P value results are consistent with our graphical representation. The P value of 0.03112 is significant at the alpha level of 0.05 but not 0.01.
