Several questions, please help !!!!!

NEEDED BY 10 PM /4/24/22

Use the t-distribution /and the sample results to complete the test of the hypotheses. Use a 5%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 H0:=100H0:=100 vs Ha:

(a) Give the test statistic and the p-value. Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places. test statistic = Enter your answer in accordance to item (a) of the question statement p-value = Enter your answer in accordance to item (a) of the question statement

(b) What is the conclusion?

Reject H0H0.

Do not reject H0H0.

Question #2

The Autistic Brain Autistic children often have a small head circumference at birth, followed by a sudden and excessive increase in head circumference during the first year of life. A recent study¹ examined the brain tissue in autopsies of seven autistic male children between the ages of 22 and 1616. The mean number of neurons in the prefrontal cortex in non-autistic male children of the same age is about 1.151.15 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 1.941.94 billion with a standard deviation of 0.500.50 billion. The values in the sample are not heavily skewed. Use the tt-distribution to test whether this sample provides evidence that autistic male 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 Medical Association, November 2011; 306(18): 2001-2010.

State the null and alternative hypotheses.

Give the test statistic and the pp-value and state the conclusion of the test. Round your answer for the test statistic to two decimal places and your answer for the pp-value to three decimal places. test statistic == pp-value == Conclusion:

RejectDo

or

not reject H0H0.

Does the sample provide evidence that autistic male children have more neurons (on average) in the prefrontal cortex than non-autistic children?

Yes

No

Question#3

Getting Enough Sleep? It is generally recommended that adults sleep at least 88 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 1212 students sampled averaged 6.26.2 hours of sleep with a standard deviation of 1.701.70 hours. Assuming this sample is representative of all her students, and assuming students need at least 88 hours of sleep a night, does this provide evidence that, on average, her students are not getting enough sleep?

4 5 7 8 9 10 Hours of Sleep