# Confidence levels, significance levels and critical values

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**Finding the Critical Value**

With a significance level of $\alpha =0.075$ what is the resulting critical value of:- Find the critical value from the following confidence levels for a right-tailed test:
**Rejecting or Failing to Reject the Null Hypothesis**

The following Null Hypothesis and Alternative Hypothesis have been derived from a statement:

$H_0$: $p \leq 0.5$

$H_1$: $p$ > $0.5$

Using a significance level of $0.10$ (which corresponds to a critical value of $Z_\alpha=1.28$), and a Z-score of $Z=1.40$ relating to our Null Hypothesis;

Can we reject the Null Hypothesis?- The following Null Hypothesis and Alternative Hypothesis have been derived from a statement:

$H_0$: $\mu \geq 175 lbs$

$H_1$: $\mu$ < $175 lbs$

Using a 95% confidence level and a Z-score of Z=-1.50 relating to our Null Hypothesis;

Can we reject the Null Hypothesis? - The following claim is made.

"70% of Canadians own a pet".

Given that the test-statistic is Z=2.75, with a confidence level of 90% what can be said about the proportions of pet owners in Canada?