For a certain nationwide standardized test there are two commonly used preparation products on the market: StudyFocus an

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For a certain nationwide standardized test there are two
commonly used preparation products on the market: StudyFocus and
Prepara. A researcher in the Education department at a nearby
university wants to determine if there is any difference between
the two products on the mean score on the test by their users.
The researcher obtains the scores on the test from a random
sample of
16
users of StudyFocus and a random sample of
15
users of Prepara. (These samples are chosen
independently.) These data are shown in the table.
Scores
StudyFocus
559
,
469
,
396
,
573
,
436
,
450
,
399
,
599
,
608
,
427
,
374
,
497
,
607
,
512
,
404
,
551
Prepara
560
,
509
,
539
,
565
,
470
,
530
,
610
,
484
,
526
,
560
,
516
,
506
,
540
,
537
,
533
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Assume that the two populations of scores are approximately
normally distributed. Can the researcher conclude, at the
0.10
level of significance, that there is a difference between
the population mean of the scores on the test by the users of
StudyFocus and the population mean of the scores on the test by the
users of Prepara?
Perform a two-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal
places. (If necessary, consult a list of formulas.)
(a)
State the null hypothesis
H0
and the alternate hypothesis
H1
.
H0:
H1:
(b)
Determine the type of test statistic to use.
▼(Choose one)
(c)
Find the value of the test statistic. (Round to three or more
decimal places.)
(d)
Find the two critical values. (Round to three or more decimal
places.)
and
(e)
At the
0.10
level of significance, can the researcher conclude that
there is a difference between the mean score on the test by the
users of StudyFocus and the mean score on the test by the users of
Prepara?
Yes
No