Question

For problems 9, 10, 11, and 12, solve the problems by answering a) State the claim (use a sentence), b) H., H, and place the claim with either one of the two. c) Test statistic, show and label the formula you use. d) Find critical value(s), and reject Ho or fail to reject Ho. You may use a p-value. e) Write a formal conclusion and final statement.

​​​​​​​Please show hand written work for everything including formulas etc.

Answer 1

Solution:

Given:

Mean =

μ = $33, 600

Sample size = n = 22

Sample mean =

T = $32, 400

Sample standard deviation = s= 1520

Level of significance = 0.01

Part a) Claim:  The mean salary is $33,600

Part b) State H0 and H1:

( Claim)

Η :μ = $33, 600

Vs

H, :μ# $33, 600

Part c) test statistic:

- s/n

t = 32400 – 33600 1520/22

—1200 1520/4.690416 *

—1200 324.065089 *

t = -3,703

Part d ) Find critical values:

df =n-1=22-1=21

Two tail area =Level of significance =  0.01

tr5 t 875 test ses t Table cum. prob one-tail two-tails| 0.50 1.00 0.25 0.50 0.20 0.40 0.15 0.30 0.10 0.20 0.05 0.10 0.025 0.05 0.01 0.02 0.005 0.01 4 S in - 0.0001.000 1.376 1.963 3.078 6.314 12.71 31.82 6.66 1.0611386 1.886 4.303 6.965 925 0.000 1765 0.9781 250 1.638 2.353 3.182 4.541 15541 0.000 0.741 0.9411.190 1.5332.1322.776 3.747 4504 0.000 0.27 0.920 1.156 1.476 2015 2.571 13.365 4032 0.000 0.718 0.906 1.134 1.440 1.943 2447 3.133707 0.000 0.711 | 0.896 1.119 1415 1.895 2365 2998 3499 | 0.0000706 0.8891.108 1.3971.860 2.30E 2.86 3355 0.000 0.703 0.883 1.100 1.33 1.833 226228213250 0.000 0.00 0.879 | 1.09313721.8122228 2743169 0.000 0.697 0.876 | 1.088 1.6. 17 2.20127183126 0.000 0.6950.873 1.0831.356 1.782 2.17926813155 0.000 0.694 0.70 1.0791350 1.71 2160 2620 3.912 14 0.000 0.692 0.868 1.0761.345 1.761 2.145 2.6242.77 0.000 0.1 0.566 1.0741.3411.753 213126022.947 0.000 0.90 0.65 1.07113371746 2.120 2.5832.21 0.000 0.689 0.663 1.068 1.333 1.740 2.110 2.567 0.000 0.688 0.862 | 1.067 1330 1734 2.101 2.552 2. 78 19| 0.000 0.688 0.8611.066 1328 1728 2.0932538 2.61 20 0.000 0.687 0.860 1.064 1325 1.725 2.086 2528 2345 21|| | 6600-80 L.053 | 1323 17212.0L 359 2.831 15 2. 96

t critical values = ( -2.831 , 2.831 )

Decision rule: Reject H0, if t test statistic value < -2.831 or > 2.831,otherwise we fail to reject H0.

Since t test statistic value = < t critical values = -2.831 , we reject null hypothesis H0.

t = -3,703

Part e) Conclusion:

Since we have rejected H0, there is not sufficient evidence to support the claim that mean salary is $33,600.

Thus mean salaries of Teachers is different from claimed mean salary $33,600.