(10) The dotpiot below is a randomization distribution of 3,000 randomization sample differences in means based on the following hypotheses: Ho Hc-N = 0 VS. Ha: Hc-N> 0, where pc is mean number of finger taps per minute for a person on caffeine, and μN is mean number of finger taps per minute for a person not on caffeine. Randomization Dotplot of 1-₂, Null hypothesis: ##2 Left Tall Two Tall Right Tail 200 (b) 150 100 50 -1 IC-IN = 2. 3 IC-IN = -1, samples 1000 men-025 std error-1.307 null 0 (a) Are the following sample differences in means reasonably likely to occur, fairly unlikely to occur, or extremely unlikely to occur just by random chance, if the null hypothesis were true? CN=-4, 5 4 IcIN = 7 Use the dotplot to estimate the p-value of an observed sample statistic of (c) Using a 5% significance level, what is your formal conclusion based on the p-value you found in part (b)?
(10) The dotpiot below is a randomization distribution of 3,000 randomization sample differences in means based on the following hypotheses: Ho Hc-N = 0 VS. Ha: Hc-N> 0, where pc is mean number of finger taps per minute for a person on caffeine, and μN is mean number of finger taps per minute for a person not on caffeine. Randomization Dotplot of 1-₂, Null hypothesis: ##2 Left Tall Two Tall Right Tail 200 (b) 150 100 50 -1 IC-IN = 2. 3 IC-IN = -1, samples 1000 men-025 std error-1.307 null 0 (a) Are the following sample differences in means reasonably likely to occur, fairly unlikely to occur, or extremely unlikely to occur just by random chance, if the null hypothesis were true? CN=-4, 5 4 IcIN = 7 Use the dotplot to estimate the p-value of an observed sample statistic of (c) Using a 5% significance level, what is your formal conclusion based on the p-value you found in part (b)?
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![The dotplot below is a randomization distribution of 3,000 randomization sample differences in means based on the following hypotheses:
\[H_0: \mu_C - \mu_N = 0\] vs. \[H_a: \mu_C - \mu_N > 0\],
where \(\mu_C\) is the mean number of finger taps per minute for a person on caffeine, and \(\mu_N\) is the mean number of finger taps per minute for a person not on caffeine.
The graph presented is a dotplot titled "Randomization Dotplot of \(\bar{x}_C - \bar{x}_N\), Null hypothesis: \(\mu_1 = \mu_2\)." It has the following features:
- The x-axis represents the difference in sample means, ranging from -4 to 4.
- The y-axis represents frequency, with counts up to 200.
- The distribution is approximately normal, centered around 0, with a mean of -0.0057 and a standard error of 0.197.
(a) Are the following sample differences in means reasonably likely to occur, fairly unlikely to occur, or extremely unlikely to occur just by random chance, if the null hypothesis were true?
\[
\bar{x}_C - \bar{x}_N = -4, \quad \bar{x}_C - \bar{x}_N = -1, \quad \bar{x}_C - \bar{x}_N = 7
\]
(b) Use the dotplot to estimate the p-value of an observed sample statistic of \(\bar{x}_C - \bar{x}_N = 2\).
(c) Using a 5% significance level, what is your formal conclusion based on the p-value you found in part (b)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F055086f6-4d26-404b-b10d-4e78791428d4%2F6d0999ba-d2e0-484a-99ea-d67b07afc754%2F5xxuvwo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The dotplot below is a randomization distribution of 3,000 randomization sample differences in means based on the following hypotheses:
\[H_0: \mu_C - \mu_N = 0\] vs. \[H_a: \mu_C - \mu_N > 0\],
where \(\mu_C\) is the mean number of finger taps per minute for a person on caffeine, and \(\mu_N\) is the mean number of finger taps per minute for a person not on caffeine.
The graph presented is a dotplot titled "Randomization Dotplot of \(\bar{x}_C - \bar{x}_N\), Null hypothesis: \(\mu_1 = \mu_2\)." It has the following features:
- The x-axis represents the difference in sample means, ranging from -4 to 4.
- The y-axis represents frequency, with counts up to 200.
- The distribution is approximately normal, centered around 0, with a mean of -0.0057 and a standard error of 0.197.
(a) Are the following sample differences in means reasonably likely to occur, fairly unlikely to occur, or extremely unlikely to occur just by random chance, if the null hypothesis were true?
\[
\bar{x}_C - \bar{x}_N = -4, \quad \bar{x}_C - \bar{x}_N = -1, \quad \bar{x}_C - \bar{x}_N = 7
\]
(b) Use the dotplot to estimate the p-value of an observed sample statistic of \(\bar{x}_C - \bar{x}_N = 2\).
(c) Using a 5% significance level, what is your formal conclusion based on the p-value you found in part (b)?
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