9.1.1 hypothesis

The data below represent the weights of the bodies and brains of 15 species. Use a TI-83, TI-83 plus, or TI-84 calculator to find the equation of the regression line, using body weight as the independent variable and brain weight as the dependent variable. Round the slope and intercept to five decimal places. (y=ax+b) find a and b:

(y=ax+b) a= 0.00035 b=0.46145

A hospital administrator noticed a large change in the weight of babies being born at the hospital in the last few months. She randomly selected 10 babies born in the last month. Historically, babies at the hospital have had a mean weight of 7.63 pounds and a standard deviation of 1.02 pounds. To test the weights, the administrator decided to use the historical standard deviation as the population standard deviation. The hospital administrator conducts a one-mean hypothesis at the 5% significance level, to test if change in the weight of babies being born at the hospital in the last few months from 7.63 pounds. (a) Which answer choice shows the correct null and alternative hypotheses for this test? Select the correct answer below: H0:μ=7.63; Ha:μ>7.63, which is a right-tailed test. H0:μ=7.63; Ha:μ<7.63, which is a left-tailed test. H0:μ=1.02; Ha:μ≠1.02, which is a two-tailed test. H0:μ=7.63; Ha:μ≠7.63, which is a two-tailed test.

H0:μ=7.63; Ha:μ≠7.63, its a two-tailed test. The null hypothesis should be the historical mean weight of babies born at this hospital: H0:μ=7.63. The study wants to know if the mean weight of babies in the past few months is different from 7.63 pounds. This means that we just want to test if the mean is not 7.63 pounds. So, the alternative hypothesis is Ha:μ≠7.63, which is a two-tailed test.

Which of the following results in a null hypothesis p=0.48 and alternative hypothesis p>0.48? Select the correct answer below: A) A car magazine claims that 48% of car owners follow a normal maintenance schedule. A mechanic thinks this is incorrect and wants to show that the percent of car owners who follow a normal maintenance schedule is not 48%. B) A car magazine claims that at most 48% of car owners follow a normal maintenance schedule. A mechanic thinks this is incorrect and wants to show that the percent of car owners who follow a normal maintenance schedule is more than 48%. C) A car magazine claims that at least 48% of car owners follow a normal maintenance schedule. A mechanic thinks this is incorrect and wants to show that the percent of car owners who follow a normal maintenance schedule is less than 48%. D) A car magazine claims that more than 48% of car owners follow a normal maintenance schedule. A mechanic thinks this is incorrect and wants to show that the percent of car owners who follow a normal maintenance schedule is at most 48%.

B) at most 48% of car owners..... a normal maintenance schedule is more than 48%. Remember that the null hypothesis is the claim that the researcher (in this case the mechanic) is trying to reject. So the null hypothesis, p=0.48 and the alternative hypothesis p>0.48 corresponds to what the mechanic is trying to show. Thus, the car magazine claim should be that the percent is at most 48%, and the mechanic should be trying to show the percent is greater than 48%, which is the second answer choice.

A mechanic wants to show that more than 44% of car owners do not follow a normal maintenance schedule. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter p. Select the correct answer below: H0: p=0.44; Ha: p>0.44 H0: p=0.44; Ha: p≥0.44 H0: p=0.44; Ha: p≤0.44 H0: p=0.44; Ha: p<0.44

H0: p=0.44; Ha: p>0.44 Let the parameter p be used to represent the proportion. Remember that the null hypothesis is the statement already believed to be true and the alternative hypothesis is the statement that is trying to be shown. In this case, the mechanic is trying to show that more than 44% of people do not follow the maintenance schedule. So the alternative hypothesis is p>0.44. The null hypothesis always contains the equality symbol: p=0.44.

A study claims that the mean age of online dating service users is 40 years. Some researchers think this is not accurate and want to show that the mean age is not 40 years. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ. H0: μ=40; Ha: μ<40 H0: μ=40; Ha: μ>40 H0: μ≠40; Ha: μ=40

H0: μ=40; Ha: μ≠40 Let the parameter μ be used to represent the mean. Remember that the null hypothesis, H0, is the claim that researchers are trying to reject. In this case, the null hypothesis is the study's claim that μ=40. The alternative hypothesis Ha is the opposite of this, μ≠40.

The answer choices below represent different hypothesis tests. Which of the choices are one-tailed tests? Select all correct answers. Select all that apply: H0:p=0.46, Ha:p<0.46 H0:p=0.34, Ha:p≠0.34 H0:p=0.63, Ha:p≠0.63 H0:p=0.35, Ha:p≠0.35 H0:p=0.39, Ha:p<0.39

H0:p=0.46, Ha:p<0.46 H0:p=0.39, Ha:p<0.39

A recent graduate moving to a new job collected sample data of the monthly rent in dollars as well as the size in square feet of 3-bedroom apartments in an area of a city. Use a TI-83, TI-83 plus, or TI-84 calculator to find the equation of the regression line, using the size as the independent variable and the monthly rent as the dependent variable. Round the slope and intercept to two decimal places. (y=ax+b) find A and B Size Rent 1389 870 1786 711 1724 758 1667 733 1667 800 1648 841 1579 909 1546 867 1415 839 1389 930

a= -.41 b= 1466.74 (y=ax+b)

The table below contains the value of house and the amount of rental income in a year that the house brings in. Use a TI-83, TI-83 plus, or TI-84 calculator to find the equation of the regression line for predicting the rental income from the value of the house. Round the slope and intercept to two decimal places. Value Rental 170000 8500 95000 7904 127000 8944 77000 4576 210000 11232 315000 12896 190000 8320 135000 8320 270000 12480 300000 12896 310000 12480 231000 12896 145000 8320 130000 7696 241000 9152 200000 10608 200000 10000 165000 8528 225000 10400 295000 11232 Provide your answer below: y=______x+_______

a= 0.03 b=4323.82

A pediatrician and a dietitian are collaborating on a joint research paper on the nutritional value and health impacts of the snacks that children typically eat. Looking at a sample of 10 healthy snacks (e.g., fruits) they recorded the cost per ounce and calories per ounce of each. Their data has been reproduced in the table below. Calculate the correlation coefficient r. $/oz cal/oz 1.93 14.49 1.03 21.85 0.74 24.71 1.3 `9.51 1.34 15.92 0.99 19.72 0.77 13.9 1.39 15.46 1.16 16.8 0.71 13.24

r= -0.337

Agricultural scientists are testing a new pig feed to determine whether it increases the pigs' weight gain. The scientists divided a herd of 20 pigs into two random groups, in which 10 of the pigs were fed with the new feed, while the other 10 pigs were fed with the regular feed. The following table shows the weight gain in pounds after six months for 10 pigs fed with the new feed and 10 pigs fed with the regular feed. Assume that the population variances of weight gained is the same for both groups and that the weight gains are normally distributed. Let the pigs fed with the new feed be the first sample, and let the pigs fed with the regular feed be the second sample. At the 0.05 level of significance, is there evidence that the new feed increases the amount of weight gained? Find the test statistic, rounded to one decimal place, and the p-value, rounded to three decimal places.

t=3.8 pvalue=0.001

The table below gives the average life expectancy (in years) of a person from a certain country based on various years of birth. Use a TI-83, TI-83 plus, or TI-84 calculator to find the equation of the regression line, using the year as the independent variable and the average life expectancy as the dependent variable. Round the slope and intercept to one decimal place. Year of Birth Life Expectancy 2001 62.977 2002 63.368 2003 63.759 2004 64.154 2005 64.556 2006 64.966 2007 65.383 2008 65.802 2009 66.219 2010 66.625 2011 67.013 2012 67.377 2013 67.714 2014 68.021

y= ax + b a= 0.4 b= 730.7

A baseball pitcher, concerned about losing speed from his fastball, undertook a new training regimen during the offseason. His team's pitching coach measured the speed of 10 random fastballs (in miles per hour) thrown by the pitcher during spring training, and compared it with a sample of 10 random fastballs thrown during the pitcher's last start in the previous season. The results are shown in the following table. Assume that the pitcher's fastball speeds had a standard deviation of 2.1 miles per hour both before and after the training regimen and that the speeds for both time periods are normally distributed. Let the pitcher's fastball speeds in the previous season be the first sample, and let the pitcher's fastball speeds in spring training be the second sample. At the 0.05 level of significance, is there evidence that the pitcher is throwing fastballs at higher speeds? Find the test statistic, rounded to two decimal places, and the p-value, rounded to three-decimal places.

z≈−4.15 p-value is approximately 0.000. Ha:μ1<μ2. The p-value of 0.000 is less than the level of significance, 0.05. Thus, we reject the null hypothesis. There is sufficient evidence to conclude that the pitcher's fastball speed has improved.