Math Answers

(a) Identify the claim and state H0 and Ha. (b) Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test, a t-test, or a chi-square test. Explain your reasoning. (c) Choose one of the options. If convenient, use technology. Option 1: Find the critical value(s), identify the rejection region(s), and find the appropriate standardized test statistic. Option 2: Find the appropriate standardized test statistic and the P-value. (d) Decide whether to reject or fail to reject the null hypothesis. (e) Interpret the decision in the context of the original claim.

7. A researcher claims that the mean age of the residents of a small town is more than 32 years. The ages (in years) of a random sample of 36 residents are listed below. At a = 0.10, is there enough evidence to support the researcher’s claim? Assume the population standard deviation is 9 years.

41 33 47 31 26 39 19 25 23 31 39 36

41 28 33 41 44 40 30 29 46 42 53 21

29 43 46 39 35 33 42 35 43 35 24 21

(a) Identify the claim and state H0 and Ha.

(b) Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test, a t-test, or a chi-square test. Explain your reasoning.

(c) Choose one of the options. If convenient, use technology.

Option 1: Find the critical value(s), identify the rejection region(s), and find the appropriate standardized test statistic.

Option 2: Find the appropriate standardized test statistic and the P-value.

(d) Decide whether to reject or fail to reject the null hypothesis.

(e) Interpret the decision in the context of the original claim.

4. A research center claims that more than 55% of U.S. adults think that it is essential that the United States continue to be a world leader in space exploration. In a random sample of 25 U.S. adults, 64% think that it is essential that the United States continue to be a world leader in space exploration. At a = 0.05, is there enough evidence to support the center’s claim?

For this test, do the following.

(a) Identify the claim and state H0 and Ha.

(b) Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test, a t-test, or a chi-square test. Explain your reasoning.

(c) Choose one of the options. If convenient, use technology.

Option 1: Find the critical value(s), identify the rejection region(s), and find the appropriate standardized test statistic.

Option 2: Find the appropriate standardized test statistic and the P-value.

(d) Decide whether to reject or fail to reject the null hypothesis.

(e) Interpret the decision in the context of the original claim.

3. A travel agent says that the mean hotel room rate for a family of 4 in a certain resort town is at most $170. A random sample of 33 hotel room rates for families of 4 has a mean of $179 and a standard deviation of $19. At a = 0.01, is there enough evidence to reject the agent’s claim?

For this test, do the following.

(a) Identify the claim and state H0 and Ha.

(b) Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test, a t-test, or a chi-square test. Explain your reasoning.

(c) Choose one of the options. If convenient, use technology.

Option 1: Find the critical value(s), identify the rejection region(s), and find the appropriate standardized test statistic.

Option 2: Find the appropriate standardized test statistic and the P-value.

(d) Decide whether to reject or fail to reject the null hypothesis.

(e) Interpret the decision in the context of the original claim.

2.The U.S. Department of Agriculture claims that the mean annual consumption of tea by a person in the United States is 8.9 gallons. A random sample of 60 people in the United States has a mean annual tea consumption of 8.2 gallons. Assume the population standard deviation is 2.2 gallons. At a = 0.10, can you reject the claim?

Find the value of the finite population correction factor given the following N=3,000 and N=360

Identify the t-value whose number of samples n = 25, area = 0.01

n = 30 area = 0.005

n = 27 , area = 0.0025

n = 35 area = 0.0010

USE A SHORT BOND PAPER

n = 40 area = 0.0005

SHOW YOUR SOLUTIONS

T

he time

that

a laptop battery lasts in everyday use before recharge is needed

is normally

distributed, with a mean of 270 minutes

and

a standard deviation o

f 55 minutes.

a) What is the probability that the battery lasts

more than four hours?

b) What value of

battery

life in minutes is exceeded with 95 % probability?

c) What is the probability

that

the battery lasts exactly

300 minutes?

According to one survey in India, 75% of Instagram users love REELS. Suppose that 25 Instagram users (randomly selected) have been approached in the university located in vile parle. They have been asked about their status of like/ dislike the Instagram- REELS. a) What is the probability that Exactly 15 of them would agree with the claim (or said they love Insta-REELS)? b) What is the probability that Exactly 20 of them would agree with the claim (or said they love Insta-REELS)?

Find the centroid for the region bounded by y=3−e^-X, the x−axis, x=2, and the y−axis.

It is claimed that the average age of working students in a certain university is 35 years. A researcher selected a random sample of 49 working students. The computation of their ages resulted to an average of 32 years with a standard deviation of 10 years. Does this mean that the average age of the working students is different from 35 years? Use 0.05 level of significance and assure normality of population.