A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 millimeters. The company wishes to test millimeters versus millimeters, using the results of samples. Calculate the P-value if the observed statistic is Round your answer to four decimal places (e. g. 98.7654).

The answers to the questions are

(a) P = 0.0176

(b)  P = 0.5

(c)  P = 0.0571

Step-by-step explanation:

The P value is the calculated probability of obtaining extreme reults which are as extreme as observed res ult when the study null hypothesis H₀ is true

The p value is given by

P ( = 185 when μ = 175)

z =  

z( = 185)  = = 1.5811

Therefore the P ( = 185 when μ = 175) =  P(z = 1.5811)  

    0.94295

The probability density function is

Therefore the probability is

= 0.0176  

b) The type II error is given by

β = P(type II error) = P(Fail to reject the null hypothesis when it is false)

Therefore

β = P ( < 185 when μ = 185)

P, which gives

P(z<0) and β = 0.5

(c) For true mean foam height of 195 mm we have

β = P ( < 185 when μ = 195)

and P

Which gives P(z < -1.58)

From z table the probability is       β = 0.0571

54 km / hours

step-by-step explanation:

we need to convert seconds to hours

60 seconds = 1 minutes

60 minutes = 1hour

15 m         60 second   60 minutes

  * *         = 54000 meters/ hour

second     1 minute             1 hour

now we need to convert meters to km

1000 m = 1 km

54000 m       1 km

*   = 54 km / hours

hour               1000m

the answer is d

hope this