A Rough Road to the End (starring corrgram()!)

 

Part I:

A.      Null hypothesis: The cookie-making machine is making less than 70 cookies.

Alternative hypothesis: The cookie-making machine is making either exactly 70, or more than 70 cookies.

B.      Z = (M – μ) / √(σ^2 / n)

= (69.1 – 69) ) / √((3.5)^2 / 55)

= (69.1 – 69) ) / √(12.25/ 55)

= 0.1 / 0.47

Z = 0.21 (Greater than LOS of 0.05, so null hypothesis is not rejected.)

C.

A p-value of ~0.58 is mostly neutral, not leaning greatly towards 1 nor 0. Therefore, it is not statistically significant and the null hypothesis cannot be rejected.

D.      Z = (M – μ) / √(σ^2 / n)

= (69.1 – 69) ) / √((1.75)^2 / 55)

= (69.1 – 69) ) / √(3.06/55)

= 0.1 / 0.0556

Z = 1.79 (Greater than LOS of 0.05, so null hypothesis is still not rejected.)

E.      Z = (M – μ) / √(σ^2 / n)

= (69 – 69) ) / √((3.5)^2 / 55)

= (69 – 69) ) / √(12.25/ 55)

= 0 / 0.47

Z = 0 (Less than LOS of 0.05, so null hypothesis is rejected.)

Part II:

Part III: