An engineer who is studying the tensile strength of a steel alloy intended for use in golf club shafts knows that tensile strength is approximately normally distributed withσ = 70 psi. A random sample of 12 specimens has a mean ten-sile strength of x = 3450 psi.

(a) Test the hypothesis that mean strength is 3500 psi. Use α = 0.05.
(b) What is the smallest level of significance at which you would be willing to reject the null hypothesis?
(c) What is the β-error for the test in part (a) if the true mean is 3470?
(d) Suppose that you wanted to reject the null hypothesis with probability at least 0.8 if mean strength μ = 3470. What sample size should be used?
(e) Explain how you could answer the question in part (a) with a two-sided confidence interval on mean tensile strength.

Hye ryung is the president of the local chapter of the american medical students association (amsa). she is organizing local outreach and informational meetings. at her first meeting there are five people present (including herself). every month after that her group grows by 5 people. a. how many members are in the group after 6 months? b. the logistics of hosting and feeding her group at meetings was more complicated than expected. the cost of feeding 5 people at her first meeting was $30, for 10 people it was $35, for 15 it was $45, and after 6 months all of the costs had added up to $100. write a function to model the cost with the number of people attending meetings. c. what connections can you make between the linear growth of the group’s membership and the increasing costs of running meetings?

The sum of the reciprocal of a positive number and the reciprocal of 2 more than the number is 3/4 equation: the number is

Math it's appreciated. (picture provided)