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33 . The screening test has a 20 percent probability of a Type II error, meaning that 20 percent of the time, it will fail to detect TB when it is in fact present.

34 . Eighty percent of the time, the screening test will detect TB when it is actually present.

9.3: distribution needed for hypothesis testing

35 . The Student’s t -test.

36 . The normal distribution or z -test.

37 . The normal distribution with μ = p and σ = p q n

38 . t 24 . You use the t -distribution because you don’t know the population standard deviation, and the degrees of freedom are 24 because df = n – 1.

39 . X ¯ ~ N ( 0.95 , 0.051 100 )
Because you know the population standard deviation, and have a large sample, you can use the normal distribution.

9.4: rare events, the sample, decision, and conclusion

40 . Fail to reject the null hypothesis, because α p

41 . Reject the null hypothesis, because α p .

42 . H 0 : μ ≥ 29.0”
H a : μ <29.0”

43 . t 19 . Because you do not know the population standard deviation, use the t -distribution. The degrees of freedom are 19, because df = n – 1.

44 . The test statistic is –4.4721 and the p -value is 0.00013 using the calculator function TTEST.

45 . With α = 0.05, reject the null hypothesis.

46 . With α = 0.05, the p -value is almost zero using the calculator function TTEST so reject the null hypothesis.

9.5: additional information and full hypothesis test examples

47 . The level of significance is five percent.

48 . two-tailed

49 . one-tailed

50 . H 0 : p = 0.8
H a : p ≠ 0.8

51 . You will use the normal test for a single population proportion because np and nq are both greater than five.

10.1: comparing two independent population means with unknown population standard deviations

52 . They are matched (paired), because you interviewed married couples.

53 . They are independent, because participants were assigned at random to the groups.

54 . They are matched (paired), because you collected data twice from each individual.

55 . d = x ¯ 1 x ¯ 2 s p o o l e d = 4.8 4.2 1.6 = 0.375
This is a small effect size, because 0.375 falls between Cohen’s small (0.2) and medium (0.5) effect sizes.

56 . d = x ¯ 1 x ¯ 2 s p o o l e d = 5.2 4.2 1.6 = 0.625
The effect size is 0.625. By Cohen’s standard, this is a medium effect size, because it falls between the medium (0.5) and large (0.8) effect sizes.

57 . p -value<0.01.

58 . You will only reject the null hypothesis if you get a value significantly below the hypothesized mean of 110.

10.2: comparing two independent population means with known population standard deviations

59 . X ¯ 1 X ¯ 2 , i.e., the mean difference in amount spent on textbooks for the two groups.

60 . H 0 : X ¯ 1 X ¯ 2 ≤ 0
H a : X ¯ 1 X ¯ 2 >0
This could also be written as:
H 0 : X ¯ 1 X ¯ 2
H a : X ¯ 1 > X ¯ 2

61 . Using the calculator function 2-SampTtest, reject the null hypothesis. At the 5% significance level, there is sufficient evidence to conclude that the science students spend more on textbooks than the humanities students.

62 . Using the calculator function 2-SampTtest, reject the null hypothesis. At the 1% significance level, there is sufficient evidence to conclude that the science students spend more on textbooks than the humanities students.

10.3: comparing two independent population proportions

63 . H 0 : p A = p B
H a : p A p B

Questions & Answers

how can l calculate G. M from the following size 125 133 141 173 182 frequency 7 5 4 1 3
Stancy Reply
how they find mean population
Joy Reply
parts of statistics
Edwin Reply
what is a mean?
Onele Reply
given the sequence 128,64,32 find the 12th term of the sequence
Shehu Reply
12th number is 0.0625
Thangarajan
why do we use summation notation to represent set of observations
MICHAEL Reply
what is the potential outlier ?
Anik Reply
A pharmaceutical company claims that their pain reliever capsule is 70% effective. But a clinical test on this capsule showed 65 out of 100 effectiveness
jelly Reply
Part of statistics
charls Reply
how to find mean population
Dawit Reply
what is data value
Ravneet Reply
what is relative frequency
Adeyemi Reply
liner regression analysis
Swathy Reply
Proper definition of outlier?
Sumbal Reply
Extraordinary observation (too distant, high, low etc)
Petr Reply

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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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