Question

You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05.

      Ho:μ≤86.2Ho:μ≤86.2
      Ha:μ>86.2Ha:μ>86.2

You believe the population is normally distributed and you know the standard deviation is σ=16.8σ=16.8. You obtain a sample mean of ¯x=89x¯=89 for a sample of size n=72n=72.

What is the test statistic for this sample? (Report the answer accurate to three decimal places.)
test statistic =  

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =  

The p-value is... Select an answer less than (or equal to) α greater than α  

This test statistic leads to a decision to... Select an answer reject the null accept the null fail to reject the null  hypothesis.

As such, the conclusion is that... Select an answer At the 5% significance level, the data provides sufficent evidence to support the claim that the μ > 86.2. At the 5% significance level, the data provides insufficient evidence to support the claim that the μ > 86.2.

Answer 1

Solution :

This is the right tailed test,  

The null and alternative hypothesis is ,

H₀ :  $\mu$$\leq$ 86.2

H_a : $\mu$ > 86.2

Test statistic = z =

= ($\bar x$ - $\mu$ ) / $\sigma$ / $\sqrt$ n

= (89 - 86.2) / 16.8 / $\sqrt$ 72

Test statistic = z = 1.414

P(Z > 1.414) = 1-P (Z < 1.414) = 1 - 0.9213

P-value = 0.0787

α = 0.05

The p-value is greater than α .

This test statistic leads to a decision to fail to reject the null  hypothesis.

At the 5% significance level, the data provides insufficient evidence to support the claim that the μ > 86.2