The valid conclusions for the manager based on the considered test is given by: Option
<h3>When do we perform one sample z-test?</h3>
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 =
= $150 - Population standard deviation =
= $30.20 - Sample mean =
= $160 - Sample size = n = 40 > 30
- Level of significance =
= 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:

- Alternate hypothesis: Assumes that customer spends more in his store than the national average. Symbolically

where
is the hypothesized population mean of the money his customer spends in his store.
The z-test statistic we get is:

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:
brainly.com/question/21477856
<span>30% of $2,341.90 is $702.57.
(0.3 * 2341.9)
Hope this helps!</span>
Answer:
x = 30.91 cm , y = 29,86 cm and z = 39.30 cm.
Total area of wood = 2942.54 cm^2.
Step-by-step explanation:
sin 15 =8/x
x = 8 / sin 15
x = 30.91 cm.
and
tan 15 = 8/y
y = 8 / tan 15
= 29.86 cm.
The value of z can be found using the Pythagoras theorem:
50^2 = x^2 + z^2
z^2 = 20^2 - x^2 = 50^2 - 30.91^2
z^2 = 1554.57
z = √1554.57
= 39.30 cm.
b. The area consists of 3 rectangles :- 1. sides x and z 2. sides z and 8 and the other has sides z and y. Also 2 triangles of height 8 and base length y cm.
Total area = 30.91 * 39.30 + 8 * 39.30 + 29.86 * 39.30 + 2 * 0.5 * 8 * 29.86
= 2942.54 cm^2.

That's about as much as you can simplify this problem.
I hope this helps! :)