Coach Elyson claims that 90% of her volleyball serves are good serves. The captain of the team thinks Coach Elyson has a lower rate of good serves. To test this, 50 of the coach's serves are randomly selected and 41 of them are good. To determine if these data provide convincing evidence that the proportion of Coach Elyson's serves that are good is less than 90%, 100 trials of a simulation are conducted. The team captain's hypotheses are: H0: p = 90% and Ha: p < 90%, where p = the true proportion of Coach Elyson's serves that are good. Based on the results of the simulation, what is an estimate of the P-value of the test?

According to a research study, parents with young children slept 6.4 hours each night last year, on average. a random sample of 18 parents with young children was surveyed and the mean amount of time per night each parent slept was 6.8. this data has a sample standard deviation of 0.9. (assume that the scores are normally distributed.) researchers conduct a one-mean hypothesis at the 5% significance level, to test if the mean amount of time parents with young children sleep per night is greater than the mean amount of time last year. the null and alternative hypotheses are h0: μ=6.4 and ha: μ> 6.4, which is a right-tailed test. the test statistic is determined to be t0=1.89 using the partial t-table below, determine the critical value(s). if there is only one critical value, leave the second answer box blank.