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The Journal de Botanique reported that the mean height of Begonias grown while being treated with a particular nutrient is 45 centimeters. To check whether this is still accurate, heights are measured for a random sample of 17 Begonias grown while being treated with the nutrient. The sample mean and sample standard deviation of those height measurements are 47 centimeters and 8 centimeters, respectively. Assume that the heights of treated Begonias are approximately normally distributed. Based on the sample, can it be concluded that the population mean height of treated begonias, p, is different from that reported in the journal? Use the 0.10 level of significance. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H0 and the alternative hypothesis H1. H0 : I] H1:|:l (b) Determine the type of test statistic to use. (Choose one) V E|=E| EISEI EIZEI (c) Find the value of the test statistic. (Round to three or more decimal places.) III (d) Find the p-value. (Round to three or more decimal places.) III (e) Can it be concluded that the mean height of treated Begonias is different from that reported in the journal? Ell2l Ell2l xo? Yes No Thanks to an initiative to recruit top students, an administrator at a college claims that this year's entering class must have a greater mean IQ score than that of entering classes from previous years. The administrator tests a random sample of 14 of this year's entering students and nds that their mean IQ score is 114, with a standard deviation of 13. The college records indicate that the mean IQ score for entering students from previous years is 111. Is there enough evidence to conclude, at the 0.05 level of signicance, that the population mean IQ score, p., of this year's class is greater than that of previous years? To answer, assume that the IQ scores of this year's entering class are approximately normally distributed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H0 and the alternative hypothesis H1- H0 : I] len (b) Determine the type of test statistic to use. (Choose one) V (c) Find the value of the test statistic. (Round to three or more decimal places.) I] (d) Find the p-value. (Round to three or more decimal places.) I] (e) Can we conclude that the mean IQ score of this year's class is greater than that of previous years? "Yes 'No (Chooseone) V l:l=l:l EISEI Elel (c) Find the value of the test statistic. (Round to three or more decimal places.) I] (d) Find the p-value. (Round to three or more decimal places.) [I (e) Can it be concluded that the mean completion time using the new process is less than 75 minutes? \"Yes "No A college claims that the proportion, p, of students who commute more than fifteen miles to school is less than 25%. A researcher wants to test this. A random sample of 275 students at this college is selected, and it is found that 51 commute more than fifteen miles to school. Is there enough evidence to support the college's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H. p H : I X S p H , :0 (b) Determine the type of test statistic to use. (Choose one) 0=0 030 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0* 0 X (d) Find the p-value. (Round to three or more decimal places.) ? 0 (e) Is there enough evidence to support the claim that the proportion of students who commute more than fifteen miles to school is less than 25%? Yes ONoBased on their records, a hospital claims that the proportion, p, of full-term babies born in the community that weigh more than 7 pounds is 47%. A pediatrician who works with several hospitals in the community would like to verify the hospital's claim. In a random sample of 230 babies born in the community, 87 weighed over 7 pounds. Is there enough evidence to reject the hospital's claim at the 0.10 level of significance? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H. O p H : 1 X S P H : 0 IT (b) Determine the type of test statistic to use. (Choose one) V 0=0 030 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 X 5 ? (d) Find the p-value. (Round to three or more decimal places.) (e) Can we reject the claim that the proportion of full-term babies born in the community that weigh more than 7 pounds is 47%? Yes ONoA marriage counselor has traditionally seen that the proportion p of all married couples for whom her communication program can prevent divorce is 78%. After making some recent changes, the marriage counselor now claims that her program can prevent divorce in more than 78% of married couples. In a random sample of 220 married couples who completed her program, 185 of them stayed together. Based on this sample, is there enough evidence to support the marriage counselor's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H . P H : 0 X S p H, : 0 (b) Determine the type of test statistic to use. (Choose one) V 0=0 030 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0*0 00 0 X 5 ? (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Is there enough evidence to support the marriage counselor's claim that the proportion of married couples for whom her program can prevent divorce is more than 78%? Yes ONoThe proportion p of residents in a community who recycle has traditionally been 60%. A policy maker claims that the proportion is less than 60% now that one of the recycling centers has been relocated. If 128 out of a random sample of 250 residents in the community said they recycle, is there enough evidence to support the policy maker's claim at the 0.10 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H. O P H : 1 X S P H :0 (b) Determine the type of test statistic to use. (Choose one) 0=0 030 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0*0 00 0 X 5 ? (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Is there enough evidence to support the policy maker's claim that the proportion of residents who recycle is less than 60%? Yes ONoAccording to a leasing firm's reports, the mean number of miles driven annually in its leased cars is 13,480 miles with a standard deviation of 1240 miles. The company recently starting using new contracts which require customers to have the cars serviced at their own expense. The company's owner believes the mean number of miles driven annually under the new contracts, u, is less than 13,480 miles. He takes a random sample of 80 cars under the new contracts. The cars in the sample had a mean of 13,280 annual miles driven. Is there support for the claim, at the 0.01 level of signicance, that the population mean number of miles driven annually by cars under the new contracts, is less than 13,480 miles? Assume that the population standard deviation of miles driven annually was not affected by the change to the contracts. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H0 and the alternative hypothesis H1. H0 : I] le (b) Determine the type of test statistic to use. >l2| xo? Yes No Maya recently switched her primary doctor to one specializing in caring for elderly patients. On her new doctor's website, it says that the mean systolic blood pressure among elderly females is 120 millimeters of mercury (mmHg). Maya believes the value is actually higher. She bases her belief on a recently reported study of 17 randomly selected, elderly females. The sample mean systolic blood pressure was 131 mmHg, and the sample standard deviation was 20 mmHg. Assume that the systolic blood pressures of elderly females are approximately normally distributed. Based on the study, at the 0.05 level of significance, can it be concluded that u, the population mean systolic blood pressure among elderly females, is greater than 120 mmHg? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H. O P Ho : I X S p (b) Determine the type of test statistic to use. (Choose one) 0=0 030 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0*0 00 0 X 5 ? (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can it be concluded that the mean systolic blood pressure among elderly females is greater than 120 mmHg? Yes ONoA decade-old study found that the proportion,p, of high school seniors who believed that "getting rich" was an important personal goal was 80%. A researcher decides to test whether or not that percentage still stands. He nds that, among the 230 high school seniors in his random sample, 168 believe that "getting rich" is an important goal. Can he conclude, at the 0.05 level of significance, that the proportion has indeed changed? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H0 and the alternative hypothesis H1. H0 : I] H1:I:I (b) Determine the type of test statistic to use. > (Chooseone) V |I|=|Il EISEI D21] (c) Find the value of the test statistic. (Round to three or more decimal places.) I] (d) Find the p-value. (Round to three or more decimal places.) I] (e) Can we conclude that the proportion of high school seniors who believe that "getting rich" is an important goal has changed? ElatEl |:l|:| x53? \"Yes\"No