Question 1 Please be careful with the rounding and try to use all decimal places when possible

A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. Of the30tires surveyed, the mean lifespan was45,600miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly consistent with the claim?

part a

State the distribution to use for the test. (Round your answers to two decimal places.)

X~______(_________,_________)

part b I have figured out that its supposed to be a z distribution but i'm stuck past that

What is the test statistic? (Round your answers to two decimal places.)

z=_________________

part c

What is thep-value? (Round your answer to four decimal places.)

p=___________

Part d

Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper bounds to the nearest whole number.)

Lower Bound =__________ Point Estimate=_______________ Upper Bound=_______________

Question 2 Please be careful with the rounding and try to use all decimal places when possible

The mean number of English courses taken in a two-year time period by male and female college students is believed to be about the same. An experiment is conducted and data are collected from29 malesand16 females.The males took an average ofthreeEnglish courses with a standard deviation of0.8. The females took an average offourEnglish courses with a standard deviation of1.0. Are the means statistically the same? (Use= 0.05)

NOTE: If you are using a Student'st-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

part a

State the distribution to use for the test.(Enter your answer in the form t_dfwheredfis the degrees of freedom. Round your answer to two decimal places.)

_________

Part b I know that this one is a t distribution but I need help past that

What is the test statistic? (Round your answer to three decimal places.)

t=__________

Part c

What is thep-value? (Round your answer to four decimal places.)

p=___________

Thank you for your help it is much appreciated!!