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Test the claim about the population mean, \( \mu \), at the given level of significance using the given sample statistics. Claim: \( \mu \neq 6000 ; \alpha=0.05 ; \sigma=373 \). Sample statistics: \( \bar{x}=5900, n=50 \) Identify the null and alternative hypotheses. Choose the correct answer below. \( \begin{array}{ll}H_{0}: \mu \leq 6000 & \text { B. } H_{0}: \mu \geq 6000 \\ H_{a}: \mu \neq 6000 & H_{a}: \mu \neq 6000\end{array} \) \( \begin{array}{ll}H_{0}: \mu \neq 6000 & H_{0}: \mu \neq 6000\end{array} \) \( H_{a}: \mu=6000 \) \( H_{0}: \mu=6000 \) \( H_{a}: \mu \neq 6000 \)

1. Thanksgiving is often an indicator that Fall has come and Winter is on the way. Below is a random sample of high temperatures in South Carolina on Thanksgiving Day from 1938 through 2020 in degrees Fahrenheit. 63 70 73

Test the claim about the population mean, \( \mu \), at the given level of significance using the given sample statistics. Claim: \( \mu \neq 7000 ; \alpha=0.05 ; \sigma=368 \). Sample statistics: \( \bar{x}=7100, n=49 \) Identify the null and alternative hypotheses. Choose the correct answer below. \( \begin{aligned} \text { A. } H_{0}: \mu \neq 7000 & \\ H_{a}: \mu \geq 7000 & \text { B. } H_{0}: \mu \leq 7000 \\ H_{0}: \mu \geq 7000 & H_{a}: \mu \neq 7000\end{aligned} \) \( H_{a}: \mu \neq 7000 \) \( H_{0}: \mu \neq 7000 \) \( H_{a}: \mu=7000 \)

Select all the correct answers. Which two hypotheses can be supported with quantitative data? People who eat low-protein diets are more likely to have less muscle mass. It's ethical to eat a vegetarian diet. Eeople are happier during the summer than during the winter. Eating less salt lowers blood pressure over time.

5. En una encuesta a 100 inversionistas, se observó lo siguiente: 5 sólo poseían acciones, 15 poseían solamente valores, 70 eran propietarios de bonos, 13 poseían acciones y valores, 23 tenían valores y bonos, 10 eran propietarios de acciones y bonos, 3 invertían en las tres cosas. a) ¿Cuántos inversionistas sólo tenían bonos? b) ¿Cuántos poseían acciones o valores? c) ¿Cuántos no invertían en bonos ni en acciones?

6. Is there a difference in the average age that people get married in the United States and its close neighbor, Canada? Suppose a random sample of 30 Americans had an average age of marriage of 28 years with standard deviation 3 years. For a random sample of 30 Canadians, the average age was 30.1 years with standard deviation 3.3 years. (a) Construct a \( 95 \% \) confidence interval for the difference in average age of marriage between Canadians and Americans. (b) Interpret the interval. (c) Based on the interval, do you expect there to be evidence or little to no evidence for \( H_{a} \) : \( \mu_{1} \neq \mu_{2} \) ? Explain without conducting the hypothesis test.

The Adobe School District is hiring a vice principal and has interviewed four candidates: Anna (A), Bono (B), Clark (C), and David (D). The hiring committee has indicated their preferences. \( \binom{A C D B}{8}\binom{C B A D}{1}\binom{B C D A}{3}\binom{D B C A}{6} \) Who is the winner using the plurality method?

Consider an election with three candidates with the results: \( \binom{C B A}{2}\binom{A C B}{8}\binom{B A C}{7}\binom{B C A}{2} \) Who wins the election using the Borda count method?

105. Is sea level the same along all coastal regions? To examine this a sample of 12 coastal locations in the Gulf Coast had mean sea level 5.3953 m and standard deviation 2.2559 m . A sample of 17 locations along the eastern seaboard had mean 3.4028 m and standard deviation 1.036 m . We can assume the distribution of sea level is Normal. (a) What is the point estimate for the difference in mean sea level between the Gulf Coast and eastern seaboard? (b) What is the standard error of the difference in means? (c) What is the margin of error for a \( 90 \% \) confidence interval? (d) Construct and interpret the confidence interval for the difference in mean sea level between the Gulf Coast and the eastern seaboard. (e) Based on the interval, do you expect there to be evidence or little to no evidence for \( H_{a} \) : \( \mu_{1} \neq \mu_{2} \) ? Explain without conducting the hypothesis test.

The Adobe School District is hiring a vice principal and has interviewed four candidates: Anna (A), Bono (B) Clark (C), and David (D). The hiring committee has indicated theirbreferences. \( \binom{A C D B}{8}\binom{C B A D}{1}\binom{B C D A}{3}\binom{D B C A}{6} \) Who is the winner using the plurality method?