Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. α = 0.05 for a two-tailed test.

15% of all Americans suffer from sleep apnea. A researcher suspects that a lower percentage of those who live in the inner city have sleep apnea. Of the 322 people from the inner city surveyed, 42 of them suffered from sleep apnea. What can be concluded at the level of significance of αα = 0.01? For this study, we should use Select an answer z-test for a population proportion t-test for a population mean  The null and alternative hypotheses would be:     Ho: ? p μ  Select an answer > < = ≠   (please enter a decimal)    H1: ? μ p  Select an answer ≠ > = <   (Please enter a decimal) The test statistic ? t z  =  (please show your answer to 3 decimal places.) The p-value =  (Please show your answer to 4 decimal places.) The p-value is ? > ≤  αα Based on this, we should Select an answer reject accept fail to reject  the null hypothesis. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly smaller than 15% at αα = 0.01, so…

A science teacher claims that the mean scores on a science assessment test for fourth grade boys and girls are equal. The mean score for 18 randomly selected boys is 153 with a standard deviation of 23 and the mean score for 20 randomly selected girls is 149 with a standard deviation of 30. At α=0.01, can you reject the teacher’s claim? Assume the populations are normally distributed and the variance are not equal. Include a filled out standardized test statistic formula. You may not use the following df formula for this problem

Medical Operations The director of a medical hospital feels that her surgeons perform more operations per year than the national average of 211. She selected a random sample of 15 surgeons and found that the mean number of operations they performed was 213.2. The standard deviation of the sample was 3.8. Is there enough evidence to support the director's feelings at =α0.05? Assume that the population is approximately normally distributed. Use the critical value method and tables. State the hypotheses and identify the claim. H0: Is a Claim or not a claim  H1: Is a claim or not a claim One-tailed or Two-tailed test? Critical Value(s):  Round the answer to 3 decimal places. Test Value: Round the answer to 3 decimal places. Make the decision Summarize the results.