Question

Newly purchased tires of a particular type are supposed to be filled to a pressure of 30 psi. Let m denote the true average pressure. A test is to be carried out to decide whether m differs from the target value. Determine the P-value for each of the following z test statistic values.
a. 2.10

b. -1.75

c. -.55

d. 1.41

e. -5.3

Answer 1

Answer:

a) 48.21 %

b) 45.99 %

c) 20.88 %

d) 42.07 %

e) 50 %

Note: these values represent differences between z values and the mean

Step-by-step explanation:

The test to carry out is:

Null hypothesis  H₀    is                           μ₀ = 30  

The alternative hypothesis                      m  ≠ 30

In which we already have the value of z for each case therefore we look  directly the probability in z table and carefully take into account that we had been asked for differences from the mean (0.5)

a)  z = 2.1   correspond to  0.9821  but mean value is ubicated at 0.5 then we subtract    0.9821 - 0.5  and get 0.4821   or 48.21 %

b)  z = -1.75   P(m) = 0.0401     That implies the probability of m being from that point p to the end of the tail, the difference between this point and the mean so 0.5 - 0.0401 = 0.4599 or 45.99 %

c)  z = -.55    P(m) = 0.2912    and this value  for same reason as before is 0.5 - 0.2912 = 0.2088  or 20.88 %

d)  z = 1.41     P(m) = 0.9207    0.9207 -0.5     0.4207  or  42.07 %

e)  z = -5.3   P(m) = 0    meaning there is not such value in z table is too small to compute  and difference to mean value will be 0.5  

d)  z= 1.41      P(m) =