Given α = 0.975
Calculate the right-tailed and left-tailed critical value for Z
Calculate right-tailed value:
Since α = 0.975, the area under the curve is 1 - α → 1 - 0.975 = 0.025
Our critical z value is -1.96
Excel or Google Sheets formula:
Excel or Google Sheets formula:=NORMSINV(0.025)Calculate left-tailed value:
Our critical z-value = 1.96
Excel or Google Sheets formula:
Excel or Google Sheets formula:=NORMSINV(0.975)Critical Z value table:
| z | Probability (Area under Curve) |
|---|---|
| -2.3263 | 0.01 |
| -2.0537 | 0.02 |
| -1.8808 | 0.03 |
| -1.7507 | 0.04 |
| -1.6449 | 0.05 |
| -1.5548 | 0.06 |
| -1.4758 | 0.07 |
| -1.4051 | 0.08 |
| -1.3408 | 0.09 |
| -1.2816 | 0.10 |
| -1.2265 | 0.11 |
| -1.175 | 0.12 |
| -1.1264 | 0.13 |
| -1.0803 | 0.14 |
| -1.0364 | 0.15 |
| -0.9945 | 0.16 |
| -0.9542 | 0.17 |
| -0.9154 | 0.18 |
| -0.8779 | 0.19 |
| -0.8416 | 0.20 |
| -0.8064 | 0.21 |
| -0.7722 | 0.22 |
| -0.7388 | 0.23 |
| -0.7063 | 0.24 |
| -0.6745 | 0.25 |
| -0.6433 | 0.26 |
| -0.6128 | 0.27 |
| -0.5828 | 0.28 |
| -0.5534 | 0.29 |
| -0.5244 | 0.30 |
| -0.4959 | 0.31 |
| -0.4677 | 0.32 |
| -0.4399 | 0.33 |
| -0.4125 | 0.34 |
| -0.3853 | 0.35 |
| -0.3585 | 0.36 |
| -0.3319 | 0.37 |
| -0.3055 | 0.38 |
| -0.2793 | 0.39 |
| -0.2533 | 0.40 |
| -0.2275 | 0.41 |
| -0.2019 | 0.42 |
| -0.1764 | 0.43 |
| -0.151 | 0.44 |
| -0.1257 | 0.45 |
| -0.1004 | 0.46 |
| -0.0753 | 0.47 |
| -0.0502 | 0.48 |
| -0.0251 | 0.49 |
| 0 | 0.50 |
| 0.0251 | 0.51 |
| 0.0502 | 0.52 |
| 0.0753 | 0.53 |
| 0.1004 | 0.54 |
| 0.1257 | 0.55 |
| 0.151 | 0.56 |
| 0.1764 | 0.57 |
| 0.2019 | 0.58 |
| 0.2275 | 0.59 |
| 0.2533 | 0.60 |
| 0.2793 | 0.61 |
| 0.3055 | 0.62 |
| 0.3319 | 0.63 |
| 0.3585 | 0.64 |
| 0.3853 | 0.65 |
| 0.4125 | 0.66 |
| 0.4399 | 0.67 |
| 0.4677 | 0.68 |
| 0.4959 | 0.69 |
| 0.5244 | 0.70 |
| 0.5534 | 0.71 |
| 0.5828 | 0.72 |
| 0.6128 | 0.73 |
| 0.6433 | 0.74 |
| 0.6745 | 0.75 |
| 0.7063 | 0.76 |
| 0.7388 | 0.77 |
| 0.7722 | 0.78 |
| 0.8064 | 0.79 |
| 0.8416 | 0.80 |
| 0.8779 | 0.81 |
| 0.9154 | 0.82 |
| 0.9542 | 0.83 |
| 0.9945 | 0.84 |
| 1.0364 | 0.85 |
| 1.0803 | 0.86 |
| 1.1264 | 0.87 |
| 1.175 | 0.88 |
| 1.2265 | 0.89 |
| 1.2816 | 0.90 |
| 1.3408 | 0.91 |
| 1.4051 | 0.92 |
| 1.4758 | 0.93 |
| 1.5548 | 0.94 |
| 1.6449 | 0.95 |
| 1.7507 | 0.96 |
| 1.8808 | 0.97 |
| 1.96 | 0.975 |
| -1.96 | 0.025 |
| 2.0537 | 0.98 |
| 2.3263 | 0.99 |
| -2.5758 | 0.005 |
| 2.5758 | 0.995 |
Final Answer
Right tail value = -1.96
Left tail value = 1.96
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How does the Critical Z-values Calculator work?
Free Critical Z-values Calculator - Given a probability from a normal distribution, this will generate the z-score critical value. Uses the NORMSINV Excel function.
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What 3 concepts are covered in the Critical Z-values Calculator?
areaNumber of square units covering the shapecritical valuea point on the distribution of the test statistic under the null hypothesis that defines a set of values that call for rejecting the null hypothesis. critical z-valuesExample calculations for the Critical Z-values Calculator
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