Hypothesis Tests — Practice Problems and Worked Solutions

17 worked problems

Every step is generated and checked by a computer algebra system.

1. 1.

   Compute the one-sample z test statistic.

   $${\mu }_0=10,\bar{x}=12,\sigma =4,n=16$$

   Answer: $2$

   Step-by-step solution

   1. $$z=\frac{\bar{x}-{\mu }_0}{\sigma /\sqrt{n}}$$
   2. $$=2$$
2. 2.

   Compute the one-sample z test statistic.

   $${\mu }_0=50,\bar{x}=47,\sigma =6,n=36$$

   Answer: $-3$

   Step-by-step solution

   1. $$z=\frac{\bar{x}-{\mu }_0}{\sigma /\sqrt{n}}$$
   2. $$=-3$$
3. 3.

   Compute the one-sample z test statistic.

   $${\mu }_0=100,\bar{x}=105,\sigma =10,n=25$$

   Answer: $\frac{5}{2}$

   Step-by-step solution

   1. $$z=\frac{\bar{x}-{\mu }_0}{\sigma /\sqrt{n}}$$
   2. $$=\frac{5}{2}$$
4. 4.

   Compute the one-sample z test statistic.

   $${\mu }_0=20,\bar{x}=22,\sigma =5,n=100$$

   Answer: $4$

   Step-by-step solution

   1. $$z=\frac{\bar{x}-{\mu }_0}{\sigma /\sqrt{n}}$$
   2. $$=4$$
5. 5.

   Compute the one-sample z test statistic.

   $${\mu }_0=75,\bar{x}=70,\sigma =8,n=64$$

   Answer: $-5$

   Step-by-step solution

   1. $$z=\frac{\bar{x}-{\mu }_0}{\sigma /\sqrt{n}}$$
   2. $$=-5$$
6. 6.

   Compute the one-sample z test statistic.

   $${\mu }_0=30,\bar{x}=36,\sigma =12,n=16$$

   Answer: $2$

   Step-by-step solution

   1. $$z=\frac{\bar{x}-{\mu }_0}{\sigma /\sqrt{n}}$$
   2. $$=2$$
7. 7.

   Compute the one-sample z test statistic.

   $${\mu }_0=40,\bar{x}=44,\sigma =8,n=16$$

   Answer: $2$

   Step-by-step solution

   1. $$z=\frac{\bar{x}-{\mu }_0}{\sigma /\sqrt{n}}$$
   2. $$=2$$
8. 8.

   Compute the one-sample z test statistic.

   $${\mu }_0=60,\bar{x}=57,\sigma =9,n=36$$

   Answer: $-2$

   Step-by-step solution

   1. $$z=\frac{\bar{x}-{\mu }_0}{\sigma /\sqrt{n}}$$
   2. $$=-2$$
9. 9.

   Compute the one-sample z test statistic.

   $${\mu }_0=25,\bar{x}=28,\sigma =5,n=25$$

   Answer: $3$

   Step-by-step solution

   1. $$z=\frac{\bar{x}-{\mu }_0}{\sigma /\sqrt{n}}$$
   2. $$=3$$
10. 10.

    Compute the one-sample z test statistic.

    $${\mu }_0=80,\bar{x}=88,\sigma =10,n=25$$

    Answer: $4$

    Step-by-step solution

    1. $$z=\frac{\bar{x}-{\mu }_0}{\sigma /\sqrt{n}}$$
    2. $$=4$$
11. 11.

    Compute the one-sample z test statistic.

    $${\mu }_0=15,\bar{x}=12,\sigma =6,n=4$$

    Answer: $-1$

    Step-by-step solution

    1. $$z=\frac{\bar{x}-{\mu }_0}{\sigma /\sqrt{n}}$$
    2. $$=-1$$
12. 12.

    Compute the one-sample z test statistic.

    $${\mu }_0=200,\bar{x}=210,\sigma =20,n=16$$

    Answer: $2$

    Step-by-step solution

    1. $$z=\frac{\bar{x}-{\mu }_0}{\sigma /\sqrt{n}}$$
    2. $$=2$$
13. 13.

    Compute the one-sample z test statistic.

    $${\mu }_0=35,\bar{x}=41,\sigma =12,n=4$$

    Answer: $1$

    Step-by-step solution

    1. $$z=\frac{\bar{x}-{\mu }_0}{\sigma /\sqrt{n}}$$
    2. $$=1$$
14. 14.

    Compute the one-sample z test statistic.

    $${\mu }_0=55,\bar{x}=50,\sigma =10,n=100$$

    Answer: $-5$

    Step-by-step solution

    1. $$z=\frac{\bar{x}-{\mu }_0}{\sigma /\sqrt{n}}$$
    2. $$=-5$$
15. 15.

    Compute the one-sample z test statistic.

    $${\mu }_0=90,\bar{x}=96,\sigma =15,n=25$$

    Answer: $2$

    Step-by-step solution

    1. $$z=\frac{\bar{x}-{\mu }_0}{\sigma /\sqrt{n}}$$
    2. $$=2$$
16. 16.

    Compute the one-sample z test statistic.

    $${\mu }_0=45,\bar{x}=39,\sigma =9,n=9$$

    Answer: $-2$

    Step-by-step solution

    1. $$z=\frac{\bar{x}-{\mu }_0}{\sigma /\sqrt{n}}$$
    2. $$=-2$$
17. 17.

    Compute the one-sample z test statistic.

    $${\mu }_0=110,\bar{x}=120,\sigma =25,n=25$$

    Answer: $2$

    Step-by-step solution

    1. $$z=\frac{\bar{x}-{\mu }_0}{\sigma /\sqrt{n}}$$
    2. $$=2$$

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