Respuesta :
The valid conclusions for the manager based on the considered test is given by: Option
When do we perform one sample z-test?
One sample z-test is performed if the sample size is large enough (n > 30) and we want to know if the sample comes from the specific population.
For this case, we're specified that:
- Population mean = [tex]\mu[/tex] = $150
- Population standard deviation = [tex]\sigma[/tex] = $30.20
- Sample mean = [tex]\overline{x}[/tex] = $160
- Sample size = n = 40 > 30
- Level of significance = [tex]\alpha[/tex] = 2.5% = 0.025
- We want to determine if the average customer spends more in his store than the national average.
Forming hypotheses:
- Null Hypothesis: Nullifies what we're trying to determine. Assumes that the average customer doesn't spend more in the store than the national average. Symbolically, we get: [tex]H_0: \mu_0 \leq \mu = 150[/tex]
- Alternate hypothesis: Assumes that customer spends more in his store than the national average. Symbolically [tex]H_1: \mu_0 > \mu = 150[/tex]
where [tex]\mu_0[/tex] is the hypothesized population mean of the money his customer spends in his store.
The z-test statistic we get is:
[tex]z = \dfrac{\overline{x} - \mu_0}{\sigma/\sqrt{n}} = \dfrac{160 - 150}{30.20/\sqrt{40}} \approx 2.094[/tex]
The test is single tailed, (right tailed).
The critical value of z at level of significance 0.025 is 1.96
Since we've got 2.904 > 1.96, so we reject the null hypothesis.
(as for right tailed test, we reject null hypothesis if the test statistic is > critical value).
Thus, we accept the alternate hypothesis that customer spends more in his store than the national average.
Learn more about one-sample z-test here:
https://brainly.com/question/21477856
