To test $H_{0}: \mu=80$ versus $H_{1}: \mu<80$, a simple random sample of size n=22 is obtained from a population that is known to be normally distributed.

If $\bar{x}=76.9$ and s=8.5, compute the test statistic.

To test $H_{0}: \mu=40$ versus $H_{1}: \mu>40$, a simple random sample of size n=25 is obtained from a population that is known to be normally distributed.

If $\bar{x}=42.3$ and s=4.3, compute the test statistic.

Forces with magnitudes of 85 pounds and 50 pounds act on a single point. The angle between the forces is $15^{\circ}$. Describe the resultant force.

-¿Conoce Sandra a alguien en el laboratorio?

• Sí ella conoce a c. alguien. b. nadie.

Use one or more of the six sum and difference identities to solve. Find the exact value of each expression.

$$\sin \left( 60 ^ { \circ } - 45 ^ { \circ } \right)$$

(a) What are the hypotheses in a chi-square test for independence? (b) Why do we call it a test of frequencies? (c) What distribution is used in this test? (d) How do we calculate the degrees of freedom for an $r \times c$ contingency table?

Use the test scores below.

$$81\quad 70\quad 73\quad 89\quad 68\quad 79\quad 91\quad 59\quad 77\quad 73\quad 80\quad 75\quad 88\quad 65\quad 82\quad 94\quad 77\quad 67\quad 82$$

What is a histogram of the data that uses intervals of 20?

Adult female black bears have masses from about 50 kilograms to 125 kilograms. Adult male black bears have masses from about 60 kilograms to 250 kilograms. Researchers measured the masses of five adult female black bears in their natural habitat. You can see their results in the table.

$$\begin{matrix} \text{Bear} & \text{Mass (in kg)}\\ \text{A} & \text{79}\\ \text{B} & \text{73}\\ \text{C} & \text{74}\\ \text{D} & \text{155}\\ \text{E} & \text{70}\\ \end{matrix}$$

What might have produced the anomalous data?

The harmonic mean of two numbers a and b equals $\frac{2}{\frac{1}{a}+\frac{1}{b}}.$ As you vary the length of a violin or guitar string, its pitch changes. If a full-length string is 1 unit long, then many lengths that are simple fractions produce pitches that harmonize, or sound pleasing together. The harmonic mean relates two lengths that produce harmonious sounds. Find the harmonic mean for each pair of string lengths. 1 and $\frac{1}{2}$

Determine whether the expression is a polynomial. If it is, write the polynomial in standard form. $\sqrt{x^{2}+7 x+6}$

While exergy stored in the oceans is immense, we have exploited this exergy far less than that of fossil-fuel deposits. Why?

Determine convergence or divergence by any method.

$$\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } n ^ { 2 } e ^ { - n ^ { 3 } / 3 }$$

Write each number as a percent. 1.23

To test $H_{0}: \mu=4.5$ versus $H_{1}: \mu>4.5$, a simple random sample of size n=13 is obtained from a population that is known to be normally distributed.

If $\bar{x}=4.9$ and s=1.3, compute the test statistic.