Stat test Final

an engineer claims that the mean life of a particular light bulb is 6.7 years We decided to reject the null hypothesis. how do you word this?

. There is sufficient evidence to reject the claim that the particular model of light bulb has a mean life of 6.7 years

Whenever the sample test statistic is not in the rejection region for the hypothesis test using μ=0 as the null​ hypothesis, the confidence interval from the sample data will contain?

0. These two methods of reaching a conclusion are equivalent.

The standard deviation of the Student t distribution varies with the sample size and is greater than?

1 (unlike the standard normal distribution, which has = 1).

a psychologist claims that more than 29 % suffer from professional problems due to extreme shyness. If we fail to reject the null (accept it) how would we word the conclusion?

There is not sufficient evidence to support the claim that the true proportion of the population that suffer professional problems due to extreme shyness is more than 29%.

the original claim doesn't contain an equality. you reject the null.

"the sample data supports the claim that..." this is the only case where the original claim is supported

the original claim has equality but you do not reject the null.

"there is not sufficient evidence to warrent rejection of the claim that...." "not guilty" verdict

the original claim doesn't contain an equality; you don't reject the null.

"there is sufficient evidence to support the claim that... (original claim)" "not guilty" vertict

The original claim contains the condition of equality. You reject the Null hypothesis

"there is sufficient evidence to warrent rejection of the claim that...." This is only the case in which the original claim is rejected

A researcher claims that the amounts of acetaminophen in cold tablets have a standard deviation greater than the 3.3 standard deviation that the manufacturer reports. We decided to reject the null hypothesis. how do you word this?

There is sufficient evidence to support the claim that the amount of acetaminophen in the cold tablets have a standard deviation greater than 3.3 mg.

An Entomologist claims that fewer than 4 in 1000 male fireflies are unable to produce light due to a genetic mutation. We decided to reject the null hypothesis. how do you word this?

There is sufficient evidence to support the claim that the true proportion of fireflies that are unable to produce light due to a genetic mutation is less than 4 in a thousand.

formulate a conclusion: carter motor company claims that the new sedan, vibra averages at least 30 miles per gallon in the city. We decided to reject the null hypothesis. how do you word this?

There is sufficient evidence to warrant rejection of the claim that the Vibra will average at least 30 mpg in the city.

type I error is the mistake of rejecting the null hypothesis when?

it is actually true.

The Student t critical value is larger (farther to the right), showing that with the Student t distribution, the sample evidence must be_____ before we can consider it to be significant.

more extreme

a game had 80% tuned into the game out of 27000 homes. the significance level is .01 and we want to test the claim that more than 72% tuned in. How do you identify the hypothesis', pvalue, test statistic etc?

multiply .80by 27000 to find X, N is 27000. detirnmine this claim is right tailed. "more than" so use >p use 1PropZtest plug in P, X, and N

left-tailed, use the "Area in One Tail" section and the desired column. Put a _____sign in front of the critical value.

negative

The symbol not equal s≠ is often expressed in computer science as​ <>, and this is a great reminder that an alternative hypothesis with the symbol not equals≠ corresponds to a ?

two tailed test.

When using the confidence interval method for testing a claim about μ when sigmaσ is​ ____, all three methods are equivalent and produce the same results.

unknown

how do you calculate the test statistic for: proportion is equal to .25, a population of 510 has 102 yellow pods.

use 1PropZTest, Use not equal sign for proportion N=510 X=102 p=.25

for a problem that gives you a population mean and sample mean and standard deviation, how do you compute the test statistic and p value?

use Stat,test, T test. Enter Pop mean (mu) sample mean, standard deviation and sample size. Choose appropriate tail or tails and calculate

a. when asked a question about testing a claim of equal proportions, how do you calculate? b. if the p value is large what can you conclude?

use a 2 sample proportion, Stat Test 6: 2PropZtest plug in success and sample size for both samples. Choose tail b. there is not a significant difference

for two random samples taken from normally distributed populations, how can you test the claim that the two are from populations with the same mean?

use stat, tests, 4: 2-SampTtest enter 1st sample N, Sx and mean, plug in second sample's N, Sx, and mean. Choose appropriate tail and calculate

how do you find the critical value using a t-dist table?

use t- dist. table. look for n-1, on df column. identify which significance level it corresponds to, and identify whether the value needs to be negative or positive, is a right-tailed or left tailed test?

Critical Value Method: If z is in the critical region, then reject ?

H0.

Note that​ ____is not always the significance level used for hypothesis testing decision making. A higher or lower percentage may be used based on the seriousness of an incorrect decision.

5%

advantages of pooling sample​ variances?

Confidence intervals are a little narrower. The number of degrees of freedom is a little higher. Hypothesis tests have more power.

Find the P-value for a two-tailed hypothesis test with a test statistic of z = 2.14. Decide whether to reject H0 if the level of significance is = 0.05.

For a two-tailed test, P = 2(Area right of 2.14) use: Normal CDF( 2.14, 10,000) = .0168 now multiply this number by two ( because it takes into account both tails) .0168 *2 =.0324 this is less than 5% so you should reject H0

In a study, 57 out of 104 randomly selected pregnant women correctly guessed the sex of their babies. Use this sample data to test the claim that the success rate of such guesses is no different from the 50% success rate expected with random chance guesses. Use a 0.05 significance level.

Go to Stat, test, 1-PropZtest (5) plug in p,x,n select <, >, or inequality sign and calculate. the result is .3268 this is more than .05 SO: there is not sufficient evidence to reject the claim that women who guess the sex of their babies have a success rate equal to 50%.

if the pvalue is higher than the significance level, what will you decide?

I will fail to reject the null

finding critical values in a t dist

Identify the level of significance Identify the degrees of freedom, df = n - 1. Find the critical value(s) using Table A-3 in the row with n - 1 degrees of freedom

Find the P-value for a left-tailed hypothesis test with a test statistic of z = -2.23. Decide whether to reject H0 if the level of significance is = 0.01.

Normal CDF( -10000,-2.23) = .0129 this is greater than .01 so you should fail to reject H0

at most 48 % pay their bills online

P less than or equal to 48% the null contains equality so the alternative would be p is greater than .48

for a two tailed test, the critical region is in two tails so the pvalue is?

P-value = twice the area in the tail beyond the test statistic

TI-83/84 technology Use normalcdf for finding _____and use invNorm for?

P-values, Critical values

Identify the type I error and the type II error that correspond to the given hypothesis: the % of adults who have a job is equal to 88%

Reject the null hypothesis that the percentage of adults who have a job is equal to 88% when that percentage is actually equal to 88 %;

A research center claims that less than 22% of internet users in the US have a wireless network in their home. In a random sample of 100 adults, 12% said they have a wireless network in their home. At the significance level = 0.01, is there enough evidence to support the researcher's claim?

Stat, Test 1-PropZtest choose <p Z= -2.41 p =.0080 this is less than .01 so we conclude: There is sufficient evidence to reject the null hypothesis in support of the claim that less than 22% of internet users in the US have a wireless network in their home

to test a claim for a 2 prop Ztest by constructing a appropriate confidence interval, you use?

Stat, test, B "2PropZInt" for confidence %: use alpha. Subtract alpha from 1 to get % and plug into 2PropZint" to get confidence interval

Important Properties of the Student t Distribution

The Student t distribution is different for different sample sizes (see Figure 7-5 in Section 7-4).

Find the critical value t for a left-tailed test given = 0.05 and n = 21

The degrees of freedom are df = n - 1 = 21 - 1 = 20. Look up = 0.05 column from the "Area in One Tail" section. Because the test is left-tailed, the critical value is negative.

Find the critical values t and -t for a two-tailed test given = 0.05 and n = 26.

The degrees of freedom are df = n - 1 = 26 - 1 = 25. Look in the = 0.05 column from the "Area in Two Tails" section. Because the test is two-tailed, one critical value is negative and one is positive

The​ _____________ states that​ if, under a given​ assumption, the probability of a particular observed event is extremely​ small, we conclude that the assumption is probably not correct

The rare event rule

if, under a given​ assumption, the probability of a particular observed event is extremely​ small, we conclude that the assumption is probably not correct.

The rare event rule

Test Statistic for Testing a Claim About a Mean (with Not Known) requirements

The sample is a simple random sample. The value of the population standard deviation is not known. The underlying population is normally distributed or the sample size n > 30

a cereal compnay claim that the mean weight of the cereal in its packets are at least 14 ounces. the data makes us fail to reject the null hypothesis (accept it). how do we word the conclusion?

There is not sufficient evidence to reject the claim that the mean weight of the cereal packets is at least 14 oz.

a researcher claims that the proportion of americans that have seen a UFO is no more than 2 in every 10000. the conclusion is to fail to reject the null (accept the claim) . How do you word this?

There is not sufficient evidence to reject the claim that the proportion of Americans that have seen a UFO is no more than 2 in ten thousand.

Claim: A coin favors heads when​ tossed, and there are 12 heads in 26 tosses.

There is not sufficient evidence to support the claim because there are not substantially more heads than tails

the manufacturer produces refrigerator systems that are supposed to maintain a true mean temp of 49 degrees, the owner of a brewery doesn't agree and claims that he can prove the mean temperature is incorrect. the data makes us fail to reject the null hypothesis (accept it).

There is not sufficient evidence to support the claim that the mean temperature is different from 49 degrees F.

how do you use technology to find the p value for a right tailed test with n=11 and a test statistic of t= 1.399

identify n-1 = 10 use tcdf function and plug lower level, upper level and n-1. tcdf [1.399,9999,10] 1.399 is lower limit, 9999 is upper and 10 is sample size minus one

calculate test statistic: less than .30, n=1147 and X =321

Use 1 PropZTest P< .30 n=1147 x=321

test the claim of P>.4 if the test statistic is 2.11 and the significance level is .05.

Use normal cdf[2.11,10000]= .0174 the area to the right of the test statistic is the pvalue. for a right tailed test, there will only be one critical value: use the significance level in Inversenorm[.05] this will equal the critical value. Choose the positive value since this is a right tailed test

Test Statistic for Testing a Claim About a Mean (with Not Known) use TI-83/84 technology

Use tcdf( for finding P-values and invT( for finding Critical values)

We fail to reject the null hypothesis if the P-value is greater than ?

alpha

The​ P-value does not separate the critical region from the values that do not lead to rejection of the null hypothesis. The​ P-value is not a value on the horizontal​ axis, it is an ?

area

As the sample size n gets larger, the Student t distribution gets _____ to the standard normal distribution.

closer

The tails in a distribution are the extreme critical regions bounded by?

critical values.

Zogby International claims that 45% of people in the United States support making cigarettes illegal. You decide to test this claim and ask a random sample of 200 people whether they support making cigarettes illegal. Of the 200 people, 49% support such a law. At = 0.05 is there enough evidence to reject the claim?

either its 45% or its not. So choose inequality sign. find P by multiplying .49 by 200 plug in x=.98 n=200 p=.45 Z= 1.14 so you should accept the Null: there is not enough evidence to reject the claim that 45% of people in the U.S. support making cigarettes illegal

The null hypothesis​ (denoted by Upper H0​) is a statement that the value of a population parameter​ (such as​ proportion, mean, or standard​ deviation) is_____ to some claimed value.

equal

When testing claims about a population proportion, the critical value method and the P-value method are ?

equivalent and will yield the same result since both methods use the same standard deviation based on the claimed proportion p.

The​ P-value is the probability of getting a value of the test statistic that is at least as ______as the one representing the sample data.

extreme

if the significance level is .05 and the alternative is an inequality. test statistic is -1.35 what is the pvalue? how do you find the critical values?

find p value by using Normal CDF[-10000,-1.35] =answer. Multiply this answer by two to represent both tails. This equals = .1770 take .05 divide by two and now subtract from 1. use that number in inversenorm [95] and compute. use both negitive and positive to represent both tails

the level of significance is .1, find the pvalue and the criitical value if: test statistic is -1.12 and alternative is an inequality

find pvalue by using normalcdf[ -10000,-1.12]= answer multiply answer by 2 to represent both tails, this equals .2627 to find critical value divide alpha by 2 and subtract from 1. this equals .95. plug this value into inversnorm [ .95] to get : 1.65. Use both negitive and positive values (-1.65,1.65) to represent both tails

when testing gas pumps, 1280 are found to be not accurate. 5664 pumps are accurate. use a .01 significance and test the claim that less than 20% are inaccurate. find critical value too

first add pumps together to get N. (6944) then identify X (1280) and P. P will be .20 identify the tail: if its less than 20% its left tailed so use : <P plug p:,x and n into 1PropZtest. use inversnorm to find critical value. Its only one tail so do not divide alpha. inversnorm(.01) =-2.33

Research Center claims that more than 55% of U.S. adults regularly watch their local television news. You test this claim and ask a random sample of 425 adults whether they regularly watch their local news. Of the 425 adults, 255 respond yes. At α = 0.05 is there enough evidence to support the claim?

plug into Stat, Test 1-PropZtest x=255 n=425 p=.55 resulting zscore is 2.07 which is past the upper .05 rejection region. So reject by: there is enough evidence to support the claim that more than 55% of U.S. adults regularly watch their local television news.

when given values for a sample are given and the question asks you to test the claim that the sample is from a population with certain criteria, how do you compute?

plug sample values into l1, run 1 var stat. Go to stat, test, T-test, and use N, X and standard deviation in formula. Pick the appropriate tail.

p=?

population proportion

The Student t distribution has the same general bell shape as the normal distribution; its wider shape reflects the greater variability that is expected when s is used to estimate ? .

population standard deviation

right-tailed, use the "Area in One Tail" section and the desired column. Put a ______sign in front of the critical value

positive

two-tailed, use the "Area in Two Tails" section and the desired column. There will be a ______ critical value.

positive and a negative

P-value =

probability of getting a test statistic at least as extreme as the one representing the sample data value

If the​ P-value is​ small, such as 0.05 or​ less, the null hypothesis is ?

rejected

The test statistic is a value used in making a decision about the null hypothesis. It is found by converting the ______ _______​ to a score​ with the assumption that the null hypothesis is true.

sample statistic

if the pvalue is less than alpha or the z value is in the critical region there would appear to be a _____ difference between proportion of wins. if the pvalue is .3725 and alpha is .05, is there a significant difference?

significant, no

if the hypothesis test is only one tailed, how do you compute the critical value? for example, a significance level or .1 for a right tailed test?

sinply plug significance level into inversnorm, but select the appropriate + or - depending on the tail of test. Inversnorm(.1)= 1.28, use positive value because it is a right tailed test!

A hypothesis test​ (or test of​ significance) is a procedure for ______ about a property of a population.

testing a claim

The inequality symbol in the alternative hypothesis points in the direction of ?

the critical region.

Mu SubXbar

the mean of all sample means from samples of size n. This value targets the population mean, , so it is an unbiased estimator

The null hypothesis is rejected if the P-value of the test statistic is less than or equal to ?

the significance level, .

The Student t distribution has a mean of t = 0 (just as ?

the standard normal distribution has a mean of z = 0).

We fail to reject the null hypothesis if ?

the test statistic falls into the fail to reject region

The null hypothesis is rejected if? .

the test statistic falls into the rejection region.

If the sample results cannot easily occur when the null hypothesis is​_____, we conclude that the assumption is not true and reject the assumption.

true