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23 - Section 6.2 Inference for a Mean Question 17 of 21 -/1 Use the t-distribution and the sample results to complete the test of the hypotheses. Use a 5 % significance level. Assume the results come from a random sample, and if the sample size is small, assume the underlying distribution is relatively normal. Test Ho : M = 120 vs Ha : M 7/1 View Policies Current Attempt in Progress The Autistic Brain Autistic children often have a small head circumference at birth) followed by a sudden and excessive increase in head circumference duringthe rst year of life. A recent study1 examined the brain tissue in autopsies of seven autistic male children between the ages ME and 16. The mean number of neurons in the prefrontal cortex in nonautistic male children ofthe same age is about 1.15 billion. The prefrontal cortex is the part of the brain most disrupted in autism, as it deals with language and social communication. In the sample of seven autistic children, the mean number of neurons in the prefrontal cortex was 1.94 billion with a standard deviation of 0.50 billion. The values in the sample are not heavily skewed. Use the Idistribution to test whether this sample provides evidence that autisticmale children have more neurons (on average) in the prefrontal cortex than non-autistic children. (This study indicates that the causes of autism may be present before birth.) 1Adapted from Courchesne,E., et.al., "Neuron Number and Size in Prefrontal Cortex of Children with Autism,\" Journal of the American MedicalAssociatian, November 2011; 306(18): 20012010. State the null and alternative hypotheses, :: w eTextbook and Media Give the test statistic and thep-value and state the conclusion of the test. Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places. teststatistic = n p-value = n Conclusion: v H01 eTextbook and Media Does the sample provide evidence that autistic male children have more neurons (on average) in the prefrontal cortex than non- autistic children? 0 Yes 0 No eTextbook and Media Save for Later Attempts: 0 of 4 used Question List Question1 Math Fill in the Blank Question 2 Math Fill in the Blank Question 3 Math Fill in the Blank Question4 Math Fill in the Blank Question 5 Math Fill in the Blank Question 6 Math Fill in the Blank Question 7 Math Fill in the Blank Question 8 Math Fill in the Blank Question 9 Math Fill in the Blank Question 10 Math Fill in the Blank Question 11 Math Fill in the Blank Question 12 Math Fill in the Blank Question 13 Math Fill in the Blank Question 14 Math Fill in the Blank Question 15 Multipart Question 15 Multipart Question 17 Multipart Question 18 Multipart Viewing Question 19 Multipa rt Question 20 Multipart Question 21 Multipart 1 / 1 J Correct 1 / 1 J Correct 1 / 1 J Correct 1 / 1 J Correct 1 / 1 J Correct 1 / 1 J Correct 1 / 1 \" Correct 1 / 1 '/ Correct 1 / 1 \" Correct 1 / 1 J Correct 7 / 1 Not started 7 / 1 Unsubmitted work 7/ 1 Not started 1 / 1 J Correct ,/ 1 Not started ,/ 1 Not started 7 / 1 Not started 7 / 1 Not started 7 / 1 Not started 7 / 1 Not started 7 / 1 Not started 6 23 - Section 6.2 Inference for a Mean Question 20 on1 7/1 View Policies Current Attempt in Progress Getting Enough Sleep? It is generally recommended that adults sleep at least 8 hours each night, One of the authors recently asked some of her students (undergraduate and graduate students at Harvard) how many hours each had slept the previous night, curious as to whether her students are getting enough sleep. The data are displayed in Figure 1. The 12 students sampled averaged 6.2 hours of sleep with a standard deviation of 1.70 hours Assuming this sample is representative of all her students, and assuming students need at least 8 hours of sleep a night, does this provide evidence that, on average, her students are not getting enough sleep? --l Hours of Sleep Figure 1 Hours of sleep for Harvard statistics students State the null and alternative hypotheses, .. l H umll: lupl a" 251' eTextbook and Media Give the test statistic and thep-value and state the conclusion of the test. Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places. teststatistic = n p-value = a Conclusion: v H0. eTextbook and Media Does the sample provide evidence that, on average, her students are not getting enough sleep? 0 Yes 0 No eTextbook and Media Save for Later Attempts: 0 of 4 used Question List Question 1 Math Fill in the Blank Question 2 Math Fill in the Blank Question 3 Math Fill in the Blank Question4 Math Fill in the Blank Question 5 Math Fill in the Blank Question 5 Math Fill in the Blank Question 7 Math Fill in the Blank Question 8 Math Fill in the Blank Question 9 Math Fill in the Blank Question 10 Math Fill in the Blank Question 11 Math Fill in the Blank Question 12 Math Fill in the Blank Question 13 Math Fill in the Blank Question 14 Math Fill in the Blank Question 15 Multipart Question 15 Multipart Question 17 Multipart Question 18 Multipart Question 19 Multipart Viewing Question 20 Multipa rt Question 21 Multipart 1 / 1 J Correct 1 / 1 J Correct 1 / 1 \" Correct 1 / 1 J Correct 1 / 1 J Correct 1 / 1 J Correct 1 / 1 J Correct 1 / 1 J Correct 1 / 1 J Correct 1 / 1 J Correct 7/ 1 Not started 7 / 1 Unsubmitted work 7 / 1 Not started 1 / 1 J Correct 7 / 1 Not started 7 / 1 Not started 7 / 1 Not started 7/ 1 Not started 7/ 1 Not started 7/ 1 Not started 7 / 1 Not started