Respuesta :
Answer:
The pvalue of the test is 0.7188 > 0.05, which means that there is not enough statistical evidence based on the sample to dispute the results of the study published in Psychiatry Research.
Step-by-step explanation:
Test if there is enough statistical evidence based on the sample to dispute the results of the study published in Psychiatry Research:
This means that at the null hypothesis we test if the proportion is 62%, that is:
[tex]H_0: p = 0.62[/tex]
At the alternate hypothesis, we test if the proportion is different from 0.62, that is:
[tex]H_a: p \neq 0.62[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample
62% is tested at the null hypothesis:
This means that [tex]\mu = 0.62, \sigma = \sqrt{0.62*0.38}[/tex]
When a random sample of 26 autistic children were observed, 17 were found to be left-handed.
This means that [tex]n = 26, X = \frac{17}{26} = 0.6538[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.6538 - 0.62}{\frac{\sqrt{0.62*0.38}}{\sqrt{26}}}[/tex]
[tex]z = 0.36[/tex]
Pvalue of test and decision:
The pvalue of the test is the probability of a proportion that differs from the mean by at least 0.6538 - 0.62 = 0.0338, which is P(|z| > 0.36), which is two multiplied by the pvalue of z = -0.36
Looking at the z-table, z = -0.36 has a pvalue of 0.3594
2*0.3594 = 0.7188
The pvalue of the test is 0.7188 > 0.05, which means that there is not enough statistical evidence based on the sample to dispute the results of the study published in Psychiatry Research.
