Determine whether the statement is true or false if it is

Question

1. Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
In a hypothesis test, you assume the alternative hypothesis is true.

2. Use the given statement to represent a claim. Write its complement and state which H0 and which is Ha.
μ ≤ 565

3. Use the given statement to represent a claim. Write its complement and state which is H0 and which is Ha.
σ ≠ 4

4. A null and alternative hypothesis are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
H0:σ ≥ 8.9
Ha: σ< 8.9

5. Write the null and alternative hypothesis. Identify which is the claim.

A light bulb manufacturer claims that the mean life of a certain type of bulb is less than 800 hours.

6. A local chess club claims that the length of time to play a game has a standard deviation of more than 15 minutes. Write sentences describing type I and type II errors for a hypothesis test of this claim.

7. A film developer claims that the mean number of pictures developed for a camera with 24 exposures is less than 23. If a hypothesis test is performed, how should you interpret a decision that (a) rejects the null hypothesis and (b) fails to reject the null hypothesis?

8. Your medical research team is investigating the mean cost of a 30-day supply of a certain heart medication. A pharmaceutical company thinks that the mean cost is more than $71. You want to support this claim. How would you write the null and alternative hypothesis?

9. The three confidence intervals to the right represent three samplings. Decide whether each confidence interval indicates that you should reject H0. Explain your reasoning.

10. Find the P-value for the indicated hypothesis test with the given standardized test statistic, z. Decide whether to reject H0 for the given level of significance α = 0.05. A research center claims that at most 16% of families in a certain state have income below the poverty level. In a random sample of 200 families, it was found that 33 of them had income below the poverty level.

11. Match each P-value with the graph that correctly displays its area
P = 0.2611 P = 0.0614
P = 0.0307 P = 0.1492

12. Find the critical z values. Assume that the normal distribution applies.
Right-tailed test; α = 0.10
Answer: α = .10, the area under the curve is 1 - α → 1 - .10 = 0.9
The critical z value is 1.2816

13. State whether the standardized test statistic z indicates that you should reject the null hypothesis.
z = 1.211
Fail to reject H_0 because z < 1.285.
z = 1.305
Reject H_0 because z > 1.285.
z = -1.113
Fail to reject H_0 because z < 1.285.
z = -1.497
Reject H_0 because z > 1.285.

14. A random sample of 78 eight grade students' scores on a national mathematics assessment test has a mean score of 263 with a standard deviation of 30. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 260. At α = 0.08, is there enough evidence to support the administrator's claim? Complete parts (a) through (e).
Write the claim mathematically and identify H0 and Ha.

Find the standardized test statistic z, and its corresponding area.

Find the P-value
Decide whether to reject or fail to reject the null hypothesis.
Interpret your decision in the context of the original claim.

A scientist estimates that the mean nitrogen dioxide level in a city is greater than 29 parts per billion. To test this estimate, you determine the nitrogen dioxide levels for 31 randomly selected days. The results are that the sample mean is 30.1 parts per billion and the sample standard deviation is 2.6 parts per billion. At α = 0.03, can you support the scientist's estimate? Complete parts (a) through (e).

Find the critical value and identify the rejection region.

The claim is "the mean nitrogen dioxide level in Calgary is greater than 29 parts per billion.

Find the standardized test statistic.

Decide whether to reject or fail to reject the null hypothesis.

Interpret the decision in the context of the original claim.

There is not enough evidence at the 3% level of significance to support the scientist's claim that the mean nitrogen dioxide level in Calgary is greater than 29 parts per billion.

15. You believe that the mean annual kilowatt hour usage of residential customers in a certain region is less than 13,500. You find that a random sample of 33 residential customers has a mean kilowatt hour usage of 13,300 with a standard deviation of 310 kilowatt hours. You conduct a statistical experiment where H0: μ ≥ 13,500 and Ha: μ< 13,500. At α = 0.01, decide whether to reject or fail to reject the null hypothesis.

Find the critical value(s).
Find the standardized test statistic.
State your conclusion.

16. Find the critical value(s) for the indicated t-test, level of significance α, and sample size n. Left-tailed test, α = 0.01, n = 17
Area under the curve for the t-distribution.

17. State whether the standardized test statistic t indicates that you should reject the null hypothesis. Explain.
t = 1.875
Reject H0 because t < -1.827.
t = 0
Fail to reject H0 because t > -1.827.
t = -1.742
Fail to reject H0because t > -1.827.
t = -1.911
Reject H0because t < -1.827.

18. An environmentalist estimates that the mean waste recycled by adults in the country is more than 1 pound per person per day. You want to test this claim. You find that the mean waste recycled per person per day for a random sample of 11 adults in a country is 1.8 pounds and the standard deviation is 0.2 pound. At α = 0.05, can you support the claim? Assume the population is normally distributed.
Which of the following correctly states H0 and Ha?

A.      H0: μ = 1 Ha: μ> 1	B.      H0: μ = 1 Ha: μ ≠ 1	C.      H0: μ ≥ 1 Ha: μ< 1
D.      H0: μ> 1 Ha: μ ≤ 1	E.       H0: μ = 1 Ha: μ< 1	F.       H0: μ ≤ 1 Ha: μ> 1

Find the critical value(s) and identify the rejection region(s).
Find the standardized test statistic.
Decide whether to reject or fail to reject the null hypothesis.
Interpret the decision in the context of the original claim.

19. For your study on the food consumption habits of teenage males, you randomly select 10 teenage males and ask each how many 12-ounce servings of soda he drinks each day. The results are listed below. At α = 0.01, is there enough evidence to support the claim that teenage males drink fewer than three 12-ounce servings of soda per day? Assume the population is normally distributed.
3.4 2.2 2.5 2.8 1.9 2.3 2.9 3.1 3.8 1.3
Write the claim mathematically and identify H0 and Ha.
Use technology to find the P-value.
Decide whether to reject or fail to reject the null hypothesis.
Interpret the decision in the context of the original claim.

20. Decide whether the normal sampling distribution can be used, test the claim about the population proportion p at the given level of significance α using the given sample statistics.
Claim: p ≠ 0.26; α = 0.10; Sample statistics: P ^= 0.21, n = 200
State the null and alternative hypotheses.
Determine the critical value(s).
Find the z-test statistic
What is the result of the test?

21. A medical researcher says that at least 27% of adults are smokers. In a random sample of 200 adults, 22.5% say they are smokers. At α = 0.03, do you have enough evidence to reject the researcher's claim?
Write the claim mathematically and identify H0 and Ha.
H0:p ≥ 0.27 (Claim) Ha: p < 0.27
Find the critical value(s) and identify the rejection region(s).
Find the standardized test statistic.
Z=(0.225-0.27)/((.27))
Decide whether to reject or fail to reject the null hypothesis.

22. In a sample of 1784 home buyers, you find that 823 home buyers found their real estate agents through a friend. At α = 0.02, can you reject the claim that 50% of home buyers find their real estate agent through a friend?
Write the claim mathematically and identify H0 and Ha.
Find the critical value(s) and identify the rejection region(s).
Find the standardized test statistic.
Decide whether to reject or fail to reject the null hypothesis.

23. State whether the standardized test statistic X2 allows you to reject the null hypothesis.
X² = 18.301

Fail to rejectH0because X² = 18.301 is between X²> 3.940 and X²< 18.307

24. Use a 0.05 significance level to test the claim that peanut candies have weights that vary more than plain candies. The standard deviation for the weights of plain candies is 0.261. A sample of 61 peanut candies has weights with a standard deviation of 0.36. Assume the population is normally distributed.

Write the claim mathematically and identify H0 and Ha.

Find the critical value(s).Identify the rejection region(s).

Use the X²-test to find the standardized test statistic.

Decide whether to reject or fail to reject the null hypothesis.

Interpret the decision in the context of the original claim.

Does it appear that peanut candies have weights that vary more than those of plain candies?

Answer 1

For the following statistics problem, solve and provide the solution for each question by showing all the work in a Microsoft word paper. Question 1: A film developer states that the mean number of pictures developed for the camera having 24 exposures is less than 23. Whenever a hypothesis test is carried out, how must you interpret a decision that (i) refuses the null hypothesis and (ii) fails to refuse the null hypothesis? Question 2: The medical research team is investigating the mean cost of a 30-day supply of a definite heart medication. A pharmaceutical organization assumes that the mean cost is more than $71. You wish for to support this claim. Explain how would you write the null and alternative hypothesis?