An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 100 engines and the mean pressure was 4.9 lbs/square inch. Assume the standard deviation is known to be 0.6. If the valve was designed to produce a mean pressure of 4.8 lbs/square inch. Required:
a. Is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications?
b. State the null and alternative hypotheses for the above scenario.

The total ticket sales for a high school basketball game were $2,260. the ticket price for students were $2.25 less than the adult ticket price. the number of adult tickets sold was 230, and the number of student tickets sold was 180. what was the price of an adult ticket?

What is the domain of the step function f(x)=[2x]-1?

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.