(a) State the null hypothesis H, and the alternative hypothesis H₁. Ho: O H₁ :0 (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 critical value at the 0.05 level of significance. (Round to three or more H Ix a S X Do oooso 0*00<0

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A psychologist studied the alcohol consumption patterns of people in two
age groups. One group consisted of people aged 21 to 35, and the other
consisted of people aged 36 to 50. The psychologist interviewed random
and independent samples from each group. She assigned a score from o
to 100 to each individual (a score of o meant no alcohol consumption)
according to factors such as the frequency and the amount of alcohol
consumed. The results from the study are summarized below.
Age 21
Age 36
to 35
to 50
n₁ = 23
n₂=29
x₁=47.8
x₂=49.4
s=222.01 s=125.44
(The first row gives the sample sizes, the second row gives the sample
means, and the third row gives the sample variances.)
Assume that the scores of all people aged 21 to are approximately
normally distributed. Assume the same for the scores of all people aged
36 to 50.
Can we conclude, at the 0.05 significance level, that the variance of the
scores of all people aged 21 to 35, o, is greater than the variance of the
scores of all people aged 36 to 50, ²?
Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places,
and round your answers as specified below. (If necessary, consult a list
of formulas.)
(a) State the null hypothesis H, and the alternative hypothesis H₁.
Ho: O
H₁:0
(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 critical value at the 0.05 level of significance. (Round to three or more
decimal places.)
(e) Can we conclude that the variance of the scores of all people aged 21 to 35 is
greater than the variance of the scores of all people aged 36 to 50?
OYes No
μ
X
님
0*0
O
X
S
0=0 OSO
2
O<O
Р
Ś
<a
olo
ロマロ
O<O
Transcribed Image Text:A psychologist studied the alcohol consumption patterns of people in two age groups. One group consisted of people aged 21 to 35, and the other consisted of people aged 36 to 50. The psychologist interviewed random and independent samples from each group. She assigned a score from o to 100 to each individual (a score of o meant no alcohol consumption) according to factors such as the frequency and the amount of alcohol consumed. The results from the study are summarized below. Age 21 Age 36 to 35 to 50 n₁ = 23 n₂=29 x₁=47.8 x₂=49.4 s=222.01 s=125.44 (The first row gives the sample sizes, the second row gives the sample means, and the third row gives the sample variances.) Assume that the scores of all people aged 21 to are approximately normally distributed. Assume the same for the scores of all people aged 36 to 50. Can we conclude, at the 0.05 significance level, that the variance of the scores of all people aged 21 to 35, o, is greater than the variance of the scores of all people aged 36 to 50, ²? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your answers as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H₁. Ho: O H₁:0 (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 critical value at the 0.05 level of significance. (Round to three or more decimal places.) (e) Can we conclude that the variance of the scores of all people aged 21 to 35 is greater than the variance of the scores of all people aged 36 to 50? OYes No μ X 님 0*0 O X S 0=0 OSO 2 O<O Р Ś <a olo ロマロ O<O
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