Understanding confidence and significance levels

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Using sample data, it is possible to find a Z-score relating to the claim (the test-statistic).

Significance level

Left Tail Test:

. Left tail test, confidence levels, significance levels and critical values

Right Tail Test:

. Right tail test, confidence levels, significance levels and critical values

Two tailed Test:

. Two tail test, confidence levels, significance levels and critical values

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Finding the Critical Value
With a significance level of $\alpha =0.075$ $α = 0.075$ what is the resulting critical value of:
1. A right-tailed test?
2. A left-tailed test?
3. A two-tailed test?
Find the critical value from the following confidence levels for a right-tailed test:
1. 90% confidence
2. 95% confidence
3. 99% confidence
Rejecting or Failing to Reject the Null Hypothesis
The following Null Hypothesis and Alternative Hypothesis have been derived from a statement:

$H_0$ $H_{0}$ :
$p \leq 0.5$ $p \leq 0.5$

$H_1$ $H_{1}$ :
$p$ $p$ > $0.5$ $0.5$

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

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

$H_0$ $H_{0}$ :
$\mu \geq 175 lbs$ $μ \geq 175 l b s$

$H_1$ $H_{1}$ :
$\mu$ $μ$ < $175 lbs$ $175 l b s$

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?

Confidence levels, significance levels and critical values