Statistics Final Exam

TRUE OR FALSE the larger the p-value, the stronger the evidence against the null hypothesis

false, because a smaller p-value is better to reject the null hypothesis

if the confidence level does not change then, ...

the sample size increases = smaller confidence interval

if the sample size does not change then,...

the smaller the confidence level = smaller confidence interval

Assuming a normal population, use the paired t-interval procedure to obtain a 99% confidence interval for u1-u2 with the following summary stats: n=8, d(bar)= 3.125, s(d) = 2.911

-0.476 to 6.726

Summary stats are given for independent simple random samples from two populations. Use the non-pooled t-interval procedure to obtain a 95% confidence interval for u1- u2 given the following summary stats: x1= 72.6, s1= 10.9 , n1= 16 x2= 68.9, s2= 8.2, n2=12

-3.74 to 11.14

a radio show producer believes that a new proposed format would be preferred by only 15% of their current listeners. In a random sample of n=100 current listeners, 22% favored the new format. She wishes to test the null hypotheses p= 0..15. Compute the value of the test statistic.

1.960

8, 9, 7, 3, 2 find the standard deviation

3.1

496, 598, 503, 528, 565, 601, 576, 543 find the sample standard deviation

40.4

Scores on a final exam are normally distributed with a mean of 220 and a standard deviation of 24. Determine the percentage of samples of size 9 that will have mean scores within 12 points of the population mean score of 220.

86.64%

Difference between Frequency and relative frequency

Frequency is the number of times a particular distinct value occurs. Relative frequency is the ratio of the frequency of a value to the total number of observations.

type 2 error...

Not rejecting the null hypothesis when it is false

type 1 error...

Rejecting null hypothesis when it is true

TRUE OR FALSE margin of error is two times the length of the confidence interval

TRUE

A sample​ mean, sample​ size, and sample standard deviation are provided below. Use the​ one-mean t-test to perform the required hypothesis test at the 10​% significance level. x=26​, s=10​, n=32​, Ho​: mu= 27​, Ha​: mu < 27 a) determine test statistic b) determine critical value(s) c) reject or no. explain

a) -0.57 b) -1.309 c) Do not reject the null hypothesis. The data does not provide sufficient evidence to conclude the mean is less than 27.

A sample​ mean, sample​ size, and sample standard deviation are provided below. Use the​ one-mean t-test to perform the required hypothesis test at the 10​% significance level. x= 23 s= 8 n=15 Ho: u=28 Ha: u< 28 a) find the test statistic b) find p- value c) reject or no

a) -2.42 b) between 0.01 and 0.05 c) reject the null hypothesis. the data provide sufficient evidence to conclude that the mean is less than 28.

data set 10​,11​,12​,13​,14​,15​,16​,17​,18. a) find the mean b) find the median

a) 14 b) 14

44, 46, 16, 2, 47 a) determine the sample standard deviation

a) 20.7

6, 1, 8, 1, 4, 3, 0, 3, 5, 6, 2, 5 a) determine the quartiles b) determine the IQR C) find the five number summary

a) Q1= 1.5, Q2= 3.5, Q3= 5.5 B) IQR= 4 C) 0 , 1.5 , 3.5 , 5.5 , 8

A nationwide survey of 1000 adults found that 50​% of respondents favored a plan to break up the 12​ megabanks, which then controlled about 69​% of the banking industry. A) identify population and sample B) Is the percentage provided a descriptive statistic or an inferential​ statistic? Explain

a) population is all adults in the country. the sample is the 1000 adults surveyed B) The percentage is a descriptive​ statistic, since it summarizes information about how much of the sample favors breaking up the megabanks.

The​ P-value for a hypothesis test is 0.077. For each of the following significance​ levels, decide whether the null hypothesis should be rejected. a) 0.1 b) 0.05

a)Reject the null hypothesis because the​ P-value is equal to or less than the significance level. b) Do not reject the null hypothesis because the​ P-value is greater than the significance level.

Define Designed Experiment

researchers impose treatments and controls and then observe characteristics and take measurements.

Define Observational study

researchers simply observe characteristics and take​ measurements, as in a sample survey.