For conducting a​ two-tailed hypothesis test with a certain data​ set, using the smaller of n1-1 and n2-1 for the degrees of freedom results in df=​11, and the corresponding critical values are t=+-2.201. Using the formula for the exact degrees of freedom results in df=​19.063, and the corresponding critical values are t=+-2.093. How is using the critical values of t=+-2.201 more​ "conservative" than using the critical values of +-​ 2.093?

Imagine you are doing a Related-Samples t-test, and you are on Step One of the hypothesis test.  If you are doing the test with α = .05, and two tails, how would the H0 (null hypothesis) look?

A sample of 323 urban adult residents of a particular state revealed 65 who favored increasing the highway speed limit from 55 to 65 mph, whereas a sample of 177 rural residents yielded 75 who favored the increase. Does this data indicate that the sentiment for increasing the speed limit is different for the two groups of residents?   (a) Test H0: p1 − p2 = 0 versus Ha: p1 − p2 ≠ 0 using ? = 0.05, where p1 refers to the urban population. (Round your test statistic to two decimal places and your P-value to four decimal places.) z =   P-value =   State the conclusion in the problem context. Fail to reject H0. The data suggests that the sentiment for increasing the speed limit is different for the two groups of residents.Reject H0. The data suggests that the sentiment for increasing the speed limit is different for the two groups of residents.    Fail to reject H0. The data does not suggest that the sentiment for increasing the speed limit is different for the two groups of…

Heights​ (cm) and weights​ (kg) are measured for 100 randomly selected adult​ males, and range from heights of 133133 to 190190 cm and weights of 3737 to 150150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x overbarxequals=168.08168.08 ​cm, y overbaryequals=81.5781.57 ​kg, requals=0.3130.313​, ​P-valueequals=0.0020.002​, and ModifyingAbove y with caretyequals=negative 108−108plus+1.121.12x. Find the best predicted value of ModifyingAbove y with carety ​(weight) given an adult male who is 169169 cm tall. Use a 0.050.05 significance level.   The best predicted value of ModifyingAbove y with carety for an adult male who is 169169 cm tall is (answer)  kg. ​(Round to two decimal places as​ needed.)

Foofy obtained a significant Fobt from an experiment with five levels. She therefore concludes that changing every condition of the independent variable results in a significant change in the dependent variable. (a) Is she correct? Why or why not? (b) What must she now do?

Suppose that we would like to test the following hypotheses on the population correlation coefficient ρ: H0: ρ ≤ 0 and H1: ρ > 0. The sample correlation coefficient (r) for a sample with 7 observations (n = 7) on x and y is 0.35 . Then the test statistic t has a value of

Only about 18% of all people can wiggle their ears. Is this percent different for millionaires? Of the 374 millionaires surveyed, 45 could wiggle their ears. What can be concluded at the αα = 0.01 level of significance? For this study, we should use    The null and alternative hypotheses would be:  H0:H0:             (please enter a decimal)  H1:H1:             (Please enter a decimal) The test statistic     =  (please show your answer to 3 decimal places.) The p-value =  (Please show your answer to 3 decimal places.) The p-value is     αα Based on this, we should      the null hypothesis. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly different from 18% at αα = 0.01, so there is statistically significant evidence to conclude that the population proportion of millionaires who can wiggle their ears is equal to 18%. The data suggest the population proportion is not significantly different from 18% at αα = 0.01, so there is…