Question

11) α = 0.05 for a two-tailed test.
A) ±1.764 B) ±2.575 C) ±1.96 D) ±1.645

12) α = 0.09 for a right-tailed test.
A) ±1.96 B) 1.96 C) 1.34 D) ±1.34

13) α = 0.05 for a left-tailed test.
A) -1.96 B) ±1.96 C) ±1.645 D) -1.645
16) Find the critical value for a right-tailed test with α = 0.01 and n = 75.
A) 2.33 B) 1.645 C) 2.575 D) 1.96

17) Find the critical value for a two-tailed test with α = 0.01 and n = 30.
A) ±1.645 B) ±2.575 C) ±1.96 D) ±2.33

18) Find the critical value for a left-tailed test with α = 0.05 and n = 48.
A) -1.96 B) -2.575 C) -1.645 D) -2.33

19) Find the critical value for a two-tailed test with α = 0.10 and n = 100.
A) ±2.33 B) ±1.96 C) ±2.575 D) ±1.645
14) α = 0.1 for a two-tailed test.
A) ±1.645 B) ±1.4805 C) ±2.052 D) ±2.33

15) α = 0.08; H1 is μ ≠ 3.24
A) 1.75 B) ±1.75 C) 1.41 D) ±1.41

Please show work for 11 and 16. a letter for the answer for the rest is fine as I can check my work.

Answer 1

Answer)

We need to use standard normal z table to estimate the critical values

11)

Answer)

Test is two tailed.

So, first we need to divide the given significance level alpha in to two equal parts.

0.05/2 = 0.025

From z table, P(z<-1.96) = P(z>1.96) = 0.025

So, critical values are -1.96 and 1.96

12)

We have a right tailed test with 0.09 alpha.

From z table, P(z>1.34) = 0.09

So, critical value is 1.34.

13)

Left tailed test with 0.05 alpha.

From z table, P(z<-1.645) = 0.05.

16)

Here we need to use t table to estimate the critical value.

As n is given.

Degrees of freedom is = n-1 = 14

For 14 dof and 0.01 alpha, critical value t from t distribution table is 2.33