In a study, researchers wanted to measure the effect of alcohol on the hippocampal region, the portion of the brain responsible for long-term memory storage, in adolescents. The researchers randomly selected 26 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 8.87 cm³. An analysis of the sample data revealed that the hippocampal volume approximately normal with no outliers and x = 8.09 cm³ and s= 0.8 cm³. Conduct the appropriate test at the x = 0.10 level of significance. Click the icon to view the table of critical t-values. State the null and alternative hypotheses. HoiBT cm3 H₁: H cm³ (Type integers or decimals. Do not round.)

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
10/15/23,9:00 AM
wn
BH5 K7890 12B45 A78M MRB科5 H望粥= 0 0 0
0.25
01.678
-Area in
0.20 0.15 0.10 0.05
66 09
1.376
0.846
720
0.25 0.20
L-100
Poor E
f
0767
015 0.10
0
1860
YouT
1.290 1.660
1.282
-Distribution
Area in Right Tail
0.025 0.02
1.646 1.962
0.05
2.449
NİGİNİNİN cicicicici cicicicici ci
白
位位粥4
4=
0.025 0.02
0.01 0.005
2.821
Nİ SİNİcicis sedNN NNcicis ciNNNN N
2.368
7 170
NİNİNNİNİ CİCİNİN~~~~
0.0025
127.321
14.089
3.833
3.690
3.372
0.01 0.005 0.0025
0.001 0.0005
18.30
170177
7171
4507
4.297
3.852
3.787
3.356
3.31
3.261
3.252
W
3.183
3.174
3.098
Table of Critical t-Values
0.001
31.599
8.610
30年
4.781
4,221
3.9272
3.566
3.49
3.460
3.45
3.402
3.390
3.300
S0000
67890 12BH5 67890 125425 67890 H2B科5 M初粥# 颈0刀額州
Transcribed Image Text:10/15/23,9:00 AM wn BH5 K7890 12B45 A78M MRB科5 H望粥= 0 0 0 0.25 01.678 -Area in 0.20 0.15 0.10 0.05 66 09 1.376 0.846 720 0.25 0.20 L-100 Poor E f 0767 015 0.10 0 1860 YouT 1.290 1.660 1.282 -Distribution Area in Right Tail 0.025 0.02 1.646 1.962 0.05 2.449 NİGİNİNİN cicicicici cicicicici ci 白 位位粥4 4= 0.025 0.02 0.01 0.005 2.821 Nİ SİNİcicis sedNN NNcicis ciNNNN N 2.368 7 170 NİNİNNİNİ CİCİNİN~~~~ 0.0025 127.321 14.089 3.833 3.690 3.372 0.01 0.005 0.0025 0.001 0.0005 18.30 170177 7171 4507 4.297 3.852 3.787 3.356 3.31 3.261 3.252 W 3.183 3.174 3.098 Table of Critical t-Values 0.001 31.599 8.610 30年 4.781 4,221 3.9272 3.566 3.49 3.460 3.45 3.402 3.390 3.300 S0000 67890 12BH5 67890 125425 67890 H2B科5 M初粥# 颈0刀額州
In a study, researchers wanted to measure the effect of alcohol on the hippocampal region, the portion of the brain responsible for long-term memory storage, in adolescents. The researchers randomly selected 26 adolescents with
alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 8.87 cm³. An analysis of the sample data revealed that the hippocampal volume is approximately
normal with no outliers and x = 8.09 cm³ and s= 0.8 cm³. Conduct the appropriate test at the x = 0.10 level of significance.
Click the icon to view the table of critical t-values.
State the null and alternative hypotheses.
Ho: μ
H₁: μ
(Type integers or decimals. Do not round.)
cm
cm
3
3
Transcribed Image Text:In a study, researchers wanted to measure the effect of alcohol on the hippocampal region, the portion of the brain responsible for long-term memory storage, in adolescents. The researchers randomly selected 26 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 8.87 cm³. An analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and x = 8.09 cm³ and s= 0.8 cm³. Conduct the appropriate test at the x = 0.10 level of significance. Click the icon to view the table of critical t-values. State the null and alternative hypotheses. Ho: μ H₁: μ (Type integers or decimals. Do not round.) cm cm 3 3
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Follow-up Question
In a study, researchers wanted to measure the effect of alcohol on the hippocampal region, the portion of the brain responsible for long-term memory storage, in adolescents. The researchers randomly selected 26 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 8.87 cm³. An analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and \(\bar{x} = 8.09 \, \text{cm}^3\) and \(s = 0.8 \, \text{cm}^3\). Conduct the appropriate test at the \(\alpha = 0.10\) level of significance.

**State the null and alternative hypotheses.**

\(H_0: \mu = 8.87 \, \text{cm}^3\)  
\(H_1: \mu < 8.87 \, \text{cm}^3\)  
(Type integers or decimals. Do not round.)

**Identify the t-statistic.**

\(t_0 = -4.97\)  (Round to two decimal places as needed.)

**Approximate the P-value.**

The P-value is in the range \(P \text{-value} < 0.01\).

**Make a conclusion regarding the hypothesis.**

**[Dropdown options: reject, do not reject, sufficient, not sufficient, greater than, equal to, different from, less than]**

**Conclusion:**

Reject the null hypothesis. There is sufficient evidence to claim that the mean hippocampal volume is less than 8.87 cm³.
Transcribed Image Text:In a study, researchers wanted to measure the effect of alcohol on the hippocampal region, the portion of the brain responsible for long-term memory storage, in adolescents. The researchers randomly selected 26 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 8.87 cm³. An analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and \(\bar{x} = 8.09 \, \text{cm}^3\) and \(s = 0.8 \, \text{cm}^3\). Conduct the appropriate test at the \(\alpha = 0.10\) level of significance. **State the null and alternative hypotheses.** \(H_0: \mu = 8.87 \, \text{cm}^3\) \(H_1: \mu < 8.87 \, \text{cm}^3\) (Type integers or decimals. Do not round.) **Identify the t-statistic.** \(t_0 = -4.97\) (Round to two decimal places as needed.) **Approximate the P-value.** The P-value is in the range \(P \text{-value} < 0.01\). **Make a conclusion regarding the hypothesis.** **[Dropdown options: reject, do not reject, sufficient, not sufficient, greater than, equal to, different from, less than]** **Conclusion:** Reject the null hypothesis. There is sufficient evidence to claim that the mean hippocampal volume is less than 8.87 cm³.
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Follow-up Question
In a study, researchers aimed to measure the effect of alcohol on the hippocampal region, the part of the brain responsible for long-term memory storage, in adolescents. They randomly selected 26 adolescents with alcohol use disorders to examine if their hippocampal volumes were less than the normal volume of 8.87 cm³. The analysis revealed that the hippocampal volume is approximately normal with no outliers, a sample mean (\(\bar{x}\)) of 8.09 cm³, and a standard deviation (s) of 0.8 cm³. An appropriate test was conducted at the \(\alpha = 0.10\) level of significance.

**State the null and alternative hypotheses:**

- \(H_0: \mu = 8.87 \, \text{cm}^3\)
- \(H_1: \mu < 8.87 \, \text{cm}^3\)

**Identify the t-statistic:**

- \(t_0 = -4.97\) (Round to two decimal places as needed.)

**Approximate the P-value:**

- The P-value is in the range: (A drop-down menu is shown with the options)
  - 0.01 < P-value < 0.05
  - 0.05 < P-value < 0.10
  - P-value > 0.10
  - P-value < 0.01
Transcribed Image Text:In a study, researchers aimed to measure the effect of alcohol on the hippocampal region, the part of the brain responsible for long-term memory storage, in adolescents. They randomly selected 26 adolescents with alcohol use disorders to examine if their hippocampal volumes were less than the normal volume of 8.87 cm³. The analysis revealed that the hippocampal volume is approximately normal with no outliers, a sample mean (\(\bar{x}\)) of 8.09 cm³, and a standard deviation (s) of 0.8 cm³. An appropriate test was conducted at the \(\alpha = 0.10\) level of significance. **State the null and alternative hypotheses:** - \(H_0: \mu = 8.87 \, \text{cm}^3\) - \(H_1: \mu < 8.87 \, \text{cm}^3\) **Identify the t-statistic:** - \(t_0 = -4.97\) (Round to two decimal places as needed.) **Approximate the P-value:** - The P-value is in the range: (A drop-down menu is shown with the options) - 0.01 < P-value < 0.05 - 0.05 < P-value < 0.10 - P-value > 0.10 - P-value < 0.01
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Follow-up Question
In a study, researchers aimed to measure the effect of alcohol on the hippocampal region, which is the part of the brain responsible for long-term memory storage, in adolescents. The researchers randomly selected 26 adolescents with alcohol use disorders to determine whether their hippocampal volumes were less than the normal volume of \(8.87 \, \text{cm}^3\). An analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and \(\bar{x} = 8.09 \, \text{cm}^3\) and \(s = 0.8 \, \text{cm}^3\). Conduct the appropriate test at the \(\alpha = 0.10\) level of significance.
Transcribed Image Text:In a study, researchers aimed to measure the effect of alcohol on the hippocampal region, which is the part of the brain responsible for long-term memory storage, in adolescents. The researchers randomly selected 26 adolescents with alcohol use disorders to determine whether their hippocampal volumes were less than the normal volume of \(8.87 \, \text{cm}^3\). An analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and \(\bar{x} = 8.09 \, \text{cm}^3\) and \(s = 0.8 \, \text{cm}^3\). Conduct the appropriate test at the \(\alpha = 0.10\) level of significance.
Solution
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