Identify the null and alternative hypothesis in the following scenario.

Describe in words the surface whose equation is given. (assume that r is not negative.) $\theta =\frac{\pi }{4}$
a) The plane $y=-z$ where y is not negative
b) The plane $y=z$ where y and z are not negative
c) The plane $y=x$ where x and y are not negative
d) The plane $y=-x$ where y is not negative
e) The plane $x=z$ where x and y are not negative

The manager of the store in the preceding exercise calculated the residual for each point in the scatterplot and made a dotplot of the residuals.
The distribution of residuals is roughly Normal with a mean of $0 and standard deviation of $22.92.
The middle 95% of residuals should be between which two values? Use this information to give an interval of plausible values for the weekly sales revenue if 5 linear feet are allocated to the stores

Explain why t distributions tend to be flatter and more spread out than the normal distribution.

Consider two independent populations that are normally distributions. A simple random sample of ${\displaystyle n_1=41}$ from the first population showed ${\displaystyle {\bar{x}}_{11}=33}$, and a simple random of size ${\displaystyle n_2=48}$ from the second population showed
${\displaystyle {\bar{x}}_2=32}$
Suppose ${\displaystyle s_1=9s_1=9\text{and}{s}_2=10s_2=10}$, find a 98% confidence interval for ${\displaystyle {\mu }_1-{\mu }_2{\mu }_1-{\mu }_2}$. (Round answers to two decimal places.)
margin of error-?
lower limit-?
upper limit-?

1) If A and B are mutually exclusive events with $P(A)=0.3$ and $P(B)=0.5$, then $P(A\cap B)=?$
2) An experiment consists of four outcomes with $P(E_1)=0.2,P(E_2)=0.3,$ and $P(E_3)=0.4$. The probability of outcome $E_4$ is ?
3) If A and B are mutually exclusive events with $P(A)=0.3$ and $P(B)=0.5$, then $P(A\cap B)=?$
4) The empirical rule states that, for data having a bell-shaped distribution, the percentage of data values being within one standard deviation of the mean is approximately
5) If a penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is ?

The college physical education department offered an advanced first aid course last semester. The scores on the comprehensive final exam were normally distributed, and the z scores for some of the students are shown below: Robert, 1.10 Juan, 1.70 Susan, -2.00 Joel, 0.00 Jan, -0.80 Linda, 1.60 If the mean score was μ=150μ=150 with standard deviation σ=20,σ=20, what was the final exam score for each student?

Assume two normal distributions where ${\displaystyle {\mu }_1=0.0001,{\sigma }_1=0.01,{\mu }_2=-.0002,{\sigma }_2=0.015,\text{and}\rho =.45}$. Using ${\displaystyle z_s=\{.814,.259\}}$, generate ${\displaystyle z_1\text{and}{z}_2}$.