BUSI 230 HW 9.1, HW 9.2, HW 9.3, HW 9.4 Connect Exercises Week 6 solutions complete answers

BUSI 230 HW 9.1, HW 9.2, HW 9.3, HW 9.4 Connect Exercises Week 6 solutions complete answers 

 

BUSI 230 HW 9.1 Basic Principles of Hypothesis Testing Assignment 

 

The  hypothesis states that a parameter is equal to a certain value while the  hypothesis states that the parameter differs from this value.

 

Rejecting  when it is true is called a  error, and failing to reject  when it is false is called a  error.

 

Determine whether the alternate hypothesis is left-tailed, right-tailed, or two-tailed.

 

Determine whether the outcome is a Type I error, a Type II error, or a correct decision.

 

Big fish: A sample of 500 flounder of a certain species have sample mean weight 46.5 grams. Scientists want to perform a hypothesis test to determine how strong the evidence is that the mean weight differs from 45 grams. State the appropriate null and alternate hypotheses.

 

Fertilizer: A new type of fertilizer is being tested on a plot of land in an orange grove, to see whether it increases the amount of fruit produced. The mean number of pounds of fruit on this plot of land with the old fertilizer was 403 pounds. Agriculture scientists believe that the new fertilizer may decrease the yield. State the appropriate null and alternate hypotheses.

 

PC Gaming: A computer magazine editor claims that the mean cost of a gaming computer is $1,250. A test is made of  versus . The null hypothesis is rejected. State an appropriate conclusion.

 

Testing, testing: An instructor believes that the mean time that students will spend on the take home test is 8 hours. A test is made of  versus . The null hypothesis is not rejected. State an appropriate conclusion.

 

Coffee: The mean caffeine content per cup of regular coffee served at a certain coffee shop is supposed to be less than 100 milligrams. A test is made of  versus . The null hypothesis is not rejected. State an appropriate conclusion.

 

Wedding bells: A wedding planner reports that the mean wedding cost is different than $28,000. A test is made of  versus . The null hypothesis is not rejected. State an appropriate conclusion.

 

Social networking: Facebook reports that the mean number of friends of adult Facebook users is 338. A test is made of  versus . The null hypothesis is not rejected. State an appropriate conclusion.

 

Check, please: A restaurant owner claims that the mean amount spent by diners at his restaurant is more than $30. A test is made of  versus . The null hypothesis is not rejected. State an appropriate conclusion.

 

On the road again: An automobile researcher claims that the mean age of automobiles in the U.S. is . A test is made of  versus . The null hypothesis is not rejected. State an appropriate conclusion.

 

Big dogs: A veterinarian claims that the mean weight of adult German shepherd dogs is 75 pounds. A test is made of  versus . The null hypothesis is rejected. State an appropriate conclusion.

 

Air handling: The mean lifetime of a handheld leaf blower is reported to be 250 hours. A lawncare technician believes the actual lifetime to be less than  hours. A test is made of  versus . The null hypothesis is rejected. State an appropriate conclusion.

 

Type I error: A company that manufactures steel wires guarantees that the mean breaking strength (in kilonewtons) of the wires is greater than 50. They measure the strengths for a sample of wires and test  versus .

If a Type I error is made, what conclusion will be drawn regarding the mean breaking strength?

If a Type II error is made, what conclusion will be drawn regarding the mean breaking strength?

This test uses a one-tailed alternative hypothesis. Explain why a one-tailed hypothesis is more appropriate than a two-tailed hypothesis in this situation.

 

Liberty University BUSI 230 HW 9.2 Hypothesis Tests for a Population Mean, Standard Deviation Known Assignment complete solutions answers and more!

 

The  is the probability, assuming  is true, of observing a value for the test statistic that is as extreme as or more extreme than the value actually observed.

 

The smaller the -value is, the stronger the evidence against the  hypothesis becomes.

 

A test is made of : 18 versus : . A sample of size n=53 is drawn, and x=20. The population standard deviation is =8.

(a) Compute the value of the test statistic. Round the answer to at least two decimal places.

Choose the correct type of hypothesis test. Then find the critical values for =0.05 and =0.01. Round your answers to three decimal places, if necessary.

Determine whether to reject .

 

Identify the following statements as true or false.

If P=0.05, the result is statistically significant at the =0.02 level.

If P=0.05, the null hypothesis is rejected at the =0.02 level.

If P=0.05, the result is statistically significant at the =0.10 level.

If P=0.05, the null hypothesis is rejected at the =0.10 level.

 

Facebook: A study showed that two years ago, the mean time spent per visit to Facebook was 20.2 minutes. Assume the standard deviation is =4.0 minutes. Suppose that a simple random sample of 107 visits was selected this year and has a sample mean of =19.2 minutes. A social scientist is interested to know whether the mean time of Facebook visits has decreased. Use the =0.10 level of significance and the P-value method with the TI-84 calculator.

(a) State the appropriate null and alternate hypotheses.

This hypothesis test is a

(b) Compute the P-value. Round the answer to at least four decimal places.

(c) Determine whether to reject . Use the  level of significance.

 

Calibrating a scale: Making sure that the scales used by businesses in the United States are accurate is the responsibility of the National Institute for Standards and Technology (NIST) in Washington, D.C. Suppose that NIST technicians are testing a scale by using a weight known to weigh exactly 1,000 grams. The standard deviation for scale reading is known to be =2.7. They weigh this weight on the scale 62 times and read the result each time. The 62 scale readings have a sample mean of x=1000.9 grams. The scale is out of calibration if the mean scale reading differs from 1,000 grams. The technicians want to perform a hypothesis test to determine whether the scale is out of calibration. Use the =0.01 level of significance and the P-value method with the TI-84 calculator.

State the appropriate null and alternate hypotheses.

Find the P-value. Round the answer to at least four decimal places.

 

Measuring lung function: One of the measurements used to determine the health of a person's lungs is the amount of air a person can exhale under force in one second. This is called the forced expiratory volume in one second, and is abbreviated FEV1. Assume the mean FEV1 for 10-year-old boys is 2.1 liters and that the population standard deviation is =0.4. A random sample of 63 10-year-old boys who live in a community with high levels of ozone pollution are found to have a sample mean FEV1 of 1.97 liters. Can you conclude that the mean FEV1 in the high-pollution community is less than 2.1 liters? Use the =0.10 level of significance and the P-value method with the TI-84 calculator.

State the appropriate null and alternate hypotheses.

Find the P-value. Round the answer to at least four decimal places.

 

Heavy children: Are children heavier now than they were in the past? The National Health and Nutrition Examination Survey (NHANES) taken between 1999 and 2002 reported that the mean weight of six-year-old girls in the United States was 49.3 pounds. Another NHANES survey, published in 2008, reported that a sample of 192 six-year-old girls weighed between 2003 and 2006 had an average weight of 48.2 pounds. Assume the population standard deviation is =14.3 pounds. Can you conclude that the mean weight of six-year-old girls in 2006 is different from what it was in 2002? Use the =0.10 level of significance and the P-value method with the TI-84 calculator.

Compute the P-value. Round your answer to at least four decimal places.

 

Liberty University BUSI 230 HW 9.3 Hypothesis Tests for a Population Mean, Standard Deviation Unknown Assignment complete solutions answers and more!

 

Select the appropriate word or phrase to complete the sentence.

The number of degrees of freedom for the Student's t-test of a population mean is always  less than the .

 

What is the relationship between confidence intervals and hypothesis testing?

When testing  versus , if a  confidence interval does not contain , we   at the  level.

 

If we decrease the value of the significance level , we  the probability of a Type I error.

 

If we decrease the value of the significance level , we  the probability of a Type II error.

 

Is there a doctor in the house? A market research firm reported the mean annual earnings of all family practitioners in the United States was $178,258. A random sample of 57 family practitioners in Los Angeles had mean earnings of x=$192,890 with a standard deviation of $43,107. Do the data provide sufficient evidence to conclude that the mean salary for family practitioners in Los Angeles differs from the national average? Use the =0.10 level of significance and the P-value method with the TI-84 calculator.

(a) State the appropriate null and alternate hypotheses.

(b) Compute the value of the test statistic. Round the answer to two decimal places.

(c) Compute the P-value. Round the answer to four decimal places.

(d) Determine whether to reject H0.

(e) State a conclusion.

 

College tuition: The mean annual tuition and fees for a sample of 24 private colleges in California was $37,000 with a standard deviation of $7,800. A dotplot shows that it is reasonable to assume that the population is approximately normal. Can you conclude that the mean tuition and fees for private institutions in California is greater than $35,000? Use the =0.10 level of significance and the P-value method with the TI-84 Plus calculator.

(a) State the appropriate null and alternate hypotheses.

(b) Compute the value of the test statistic. Round the answer to two decimal places.

(c) Compute the -value. Round the -value to at least four decimal places.

(d) Determine whether to reject .

(e) State a conclusion.

 

Commuting to work: A community survey sampled 1923 people in Colorado and asked them how long it took them to commute to work each day. The sample mean one-way commute time was 24.6 minutes with a standard deviation of 13 minutes. A transportation engineer claims that the mean commute time is less than 25 minutes. Do the data provide convincing evidence that the engineer's claim is true? Use the =0.10 level of significance and the P-value method with the TI-84 Plus calculator.

(a) State the appropriate null and alternate hypotheses.

This hypothesis test is a

(b) Compute the value of the test statistic. Round the answer to two decimal places.

(c) Compute the -value. Round the answer to at least four decimal places.

(d) Determine whether to reject .

(e) State a conclusion.

 

Liberty University BUSI 230 HW 9.4 Hypothesis Tests for Proportions Assignment complete solutions answers and more!

 

Spam: A researcher reported that 71.8% of all email sent in a recent month was spam. A system manager at a large corporation believes that the percentage at his company may be 78%. He examines a random sample of 500 emails received at an email server, and finds that 370 of the messages are spam. Can you conclude that the percentage of emails that are spam differs from 78%? Use both =0.01 and =0.05 levels of significance and the P-value method with the TI-84 Plus calculator.

(a) State the appropriate null and alternate hypotheses.

(b) Compute the value of the test statistic. Round the answer to at least two decimal places

(c) Compute the -value. Round the answer to at least four decimal places.

(d) Determine whether to reject .

(e) State a conclusion.

 

Kids with cell phones: A marketing manager for a cell phone company claims that less than 57% of children aged 8-12 have cell phones. In a survey of 818 children aged 8-12 by a national consumers group, 450 of them had cell phones. Can you conclude that the manager's claim is true? Use the =0.05 level of significance and the P-value method with the TI-84 Plus calculator.

(a) State the appropriate null and alternate hypotheses.

Compute the test statistic. Do not round intermediate steps. Round the answer to two decimal places.

(b) Compute the P-value. Round the answer to at least four decimal places.

(c) Determine whether to reject H0.

 

Quit smoking: In a survey of 444 HIV-positive smokers, 200 reported that they had used a nicotine patch to try to quit smoking. Can you conclude that less than half of HIV-positive smokers have used a nicotine patch? Use the =0.01 level of significance and the P-value method with the TI-84 Plus calculator.

(a) State the appropriate null and alternate hypotheses.

This hypothesis test is a

Compute the test statistic. Do not round intermediate steps. Round the answer to two decimal places.

(b) Compute the P-value. Round the answer to at least four decimal places.

(c) Determine whether to reject H0.

(d) Using , can you conclude that less than half of HIV-positive smokers have used a nicotine patch?

 

Game consoles: A poll surveyed 341 video gamers, and 81 of them said that they prefer playing games on a console, rather than a computer or hand-held device. An executive at a game console manufacturing company claims that less than 27% of gamers prefer consoles. Does the poll provide convincing evidence that the claim is true? Use the =0.01 level of significance and the P-value method and Excel.

(a) State the appropriate null and alternate hypotheses.

(b)Compute the test statistic. Do not round intermediate steps. Round the answer to two decimal places.

(c)Using the result from part (b), compute the -value. Round the final answer to at least four decimal places.

(d)Determine whether to reject .

(e)State a conclusion.

 

Curing diabetes: Vertical banded gastroplasty is a surgical procedure that reduces the volume of the stomach in order to produce weight loss. In a recent study, 82 patients with Type 2 diabetes underwent this procedure, and 59 of them experienced a recovery from diabetes. Does this study provide convincing evidence that more than 63% of those with diabetes who undergo this surgery will recover from diabetes? Use the =0.10 level of significance and the P-value method and Excel.

(a) State the appropriate null and alternate hypotheses.

(b)Compute the test statistic. Do not round intermediate steps. Round the answer to two decimal places.

(c)Using the result from part (b), compute the -value. Round the final answer to at least four decimal places.

(d)Determine whether to reject .

(e)State a conclusion.