STA404 Handouts

Hypothesis · Testing · Pr · oc · ed · ur · e · General · Sorting flypsthssis-Tsding bablams god’ñianaI Mdhad)

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6ieg S State the hypotheses and identify the

claim.

Find the critical valne{s) fmm the

appropriate uble

TU Compute the ten value.

Oep A Make the decision to reject or not

reject the null hypothesis.

Summarize the results.

General · formula · format

Many hypotheses are tested using a statistical test based on the following general

formula:

Test Value — (Observed value) — (Expected value)

Standard error

The observed value is the “statistic” (such as the mean) that is computed from the

sample data.

The expected value is the “parameter” (such as the mean) that you would expect to

obtain if the null hypothesis were true. In other words, the hypothesized value.

The denominator is the standard error of the statistic being tested (in this case, the

standard error of the mean).

b —

S. E(b)

It is t-test. It depends on Degree of Freedom -— df= n-2 d.f. 95 % 98% 99°4

One tail, a 0.10 Q.Q5

0.025

0.0IH

0.20 0. IO 0.Q5 OQ1

30 i 8 6.3 I4 12.706 3I.R2J 63.637 T.ñB6 2.920 4.303 6.965 9.923 T.63B 2.3S3 3.IB2 4.541 5.B4I 1533 2.132 2.776 3./4 4.fiT)4 2.0 15 2.57I 3.365 4.032 I .440 1.943 2.447 3.143 3.70/ 1.B95 1.B6P 2.365 2.306 2.99R 2.B96 3.499 3.,55 2.R2 I 3C50 I.3•2 I .B 12 2.225 2. i64 3.169 T.k3 1.796 2J01 2.il8 3.l0fi J .356 1.7B2 2,179

2.681

3.055 I %0 1.7 7 1 2.160 2.6S0 3.012 I .345 1.76 1

2145 · 2.624 · 2.97

1 34 I 1.? S3 2.131 2.602 2.947 I .M 1.746 2.120 2.5B3 2.921 J 33S 1.740 2.110 2.567 2.B9B IB I J30 I . 34 2.101 2.552 2.R7B l9 I ,328 L72R 2.093

2.539

2.B61 l.]2S I .723 2.086 2.528 2.R45 I. 323 I .72 I 2.0Sfl 2.518 2.831 I.M1 I .717 2.074 2.508 2.f119 l.3l9 I .? I4 2.059 2.500 2.807

Critical Value, Comparison and

Conclusion

Step 5

Use t-table to find the critical values.

Plot these values on bell shaped curve.

Compare calculated value with table value

Conclude and summarize the result

- 0.025 -•-

Do not re¡ect -•- 0.025 -•-

Reject