Question

The average height of students in a freshman class of a certain school has been 168.67 cm with a population standard deviation of 8.67 cm. Is there a reason to believe that there has been a change in the average height if a random sample of 49 students in the present freshman class has an average height of 155.04 cm? Use a 0.1 level of significance.

What are the given? Write only the number. :

population mean:Blank 1 cm

population standard deviation:Blank 2 cm

sample size:Blank 3

sample mean:Blank 4 cm

level of significance:Blank 5

What are the critical values? Write the positive critical value first then the negative.

z:Blank 6 andBlank 7

What is the value of the calculated z? Round your answer to the nearest hundredths.

z:Blank 8

Answer 1

population mean: $168.67$ cm

population standard deviation: $8.67$ cm

sample size: $49$

sample mean: $155.04$ cm

level of significance: $0.1$

$z_c:$ $-1.6449$ and $1.6449$

The z-statistic is computed as follows:

$$z=\dfrac{\bar{x}-\mu}{\sigma/\sqrt{n}}=\dfrac{155.04-167.67}{8.67/\sqrt{49}}$$

$$\approx-10.20$$

z: $-10.20$