Question

12.

Calculate the critical z-value(s) for each of the given hypothesis test scenarios below. If mulitple critical values exist for a single scenario, enter the solutions using a comma-separated list. Round z-values to two decimal places.

• Find the critical z-value(s) for a left-tailed test of hypothesis for a mean, assuming the population standard deviation is known, with a sample size of 98 and let α=0.005.
• z=
• 
  
• Find the critical z-value(s) for a right-tailed test of hypothesis for a mean, assuming the population standard deviation is known, with a sample size of 53 and let α=0.025.
• z=
• Find the critical z-value(s) for a two-tailed test of hypothesis for a mean, assuming the population standard deviation is known, with a sample size of 105 and let α=0.05.
• z=
• Find the critical z-value(s) for a two-tailed test of hypothesis for a mean, assuming the population standard deviation is known, with a sample size of 51 and a signifance level of 20%.
• z=
• 
  

Answer 1

Solution,

1) n = 98

This is left-tailed test,

P(z < z ) = 0.005

= P(z < -2.58 ) = 0.005

z = -2.58

2) n = 53

This is right-tailed test,

P(z > z ) = 0.025

= 1 - P(z < z ) = 0.025

= P(z < z ) = 1 - 0.025

= P(z < z ) = 0.975

= P(z < 1.96 ) = 0.975

z = 1.96

3) n = 105

This is two-tailed test,

  = 0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96

z = -1.96, 1.96

4) n = 51

This is two-tailed test,

  = 0.20

/2 = 0.10

Z/2 = Z0.10 = 1.28

z = -1.28, 1.28