Consider the accompanying data on x = research and development expenditure (millions of dollars) and y = growth rate (% per year) for eight different industries. X 2.025 5.037 0.904 3.571 1.157 0.327 0.378 0.191 t = y 1.90 3.96 2.44 0.88 0.37 -0.90 0.49 1.01 (a) Would a simple linear regression model provide useful information for predicting growth rate from research and development expenditure? Test the appropriate hypotheses using a 0.05 significance level. Calculate the test statistic. (Round your answer to two decimal places.) Use technology to find the P-value for this test. (Round your answer to four decimal places.) P-value = What can you conclude? Fail to reject Ho. We do not have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. O Reject Ho. We do not have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. O Reject Ho. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. O Fail to reject Ho. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. (b) Use a 90% confidence interval to estimate the average change in growth rate associated with a $1,000,000 increase in expenditure. (Use technology to find the critical value. Round your answers to four decimal places.) % per yr Interpret the resulting interval. O We are 90% confident that the mean change in research and development expenditure associated with a 1 percent change in growth rate is in this interval. O We are 90% confident that the mean change in research and development expenditure associated with a 1 percent change in growth rate is outside this interval. O We are 90% confident that the mean change in growth rate associated with a $1,000 increase in research and development expenditure is in this interval. O We are 90% confident that the mean change in growth rate associated with a $1,000 increase in research and development expenditure is outside this interval.
Consider the accompanying data on x = research and development expenditure (millions of dollars) and y = growth rate (% per year) for eight different industries. X 2.025 5.037 0.904 3.571 1.157 0.327 0.378 0.191 t = y 1.90 3.96 2.44 0.88 0.37 -0.90 0.49 1.01 (a) Would a simple linear regression model provide useful information for predicting growth rate from research and development expenditure? Test the appropriate hypotheses using a 0.05 significance level. Calculate the test statistic. (Round your answer to two decimal places.) Use technology to find the P-value for this test. (Round your answer to four decimal places.) P-value = What can you conclude? Fail to reject Ho. We do not have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. O Reject Ho. We do not have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. O Reject Ho. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. O Fail to reject Ho. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. (b) Use a 90% confidence interval to estimate the average change in growth rate associated with a $1,000,000 increase in expenditure. (Use technology to find the critical value. Round your answers to four decimal places.) % per yr Interpret the resulting interval. O We are 90% confident that the mean change in research and development expenditure associated with a 1 percent change in growth rate is in this interval. O We are 90% confident that the mean change in research and development expenditure associated with a 1 percent change in growth rate is outside this interval. O We are 90% confident that the mean change in growth rate associated with a $1,000 increase in research and development expenditure is in this interval. O We are 90% confident that the mean change in growth rate associated with a $1,000 increase in research and development expenditure is outside this interval.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
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Transcribed Image Text:Consider the accompanying data on x = research and development expenditure (millions of dollars) and y = growth rate
(% per year) for eight different industries.
X 2.025 5.037 0.904 3.571 1.157 0.327 0.378 0.191
t =
y
1.90 3.96 2.44 0.88 0.37 -0.90 0.49
1.01
(a) Would a simple linear regression model provide useful information for predicting growth rate from research and
development expenditure? Test the appropriate hypotheses using a 0.05 significance level.
Calculate the test statistic. (Round your answer to two decimal places.)
Use technology to find the P-value for this test. (Round your answer to four decimal places.)
P-value =
What can you conclude?
Fail to reject Ho. We do not have convincing evidence of a useful linear relationship between growth rate and research
and development expenditure.
O Reject Ho. We do not have convincing evidence of a useful linear relationship between growth rate and research and
development expenditure.
O Reject Ho. We have convincing evidence of a useful linear relationship between growth rate and research and
development expenditure.
O Fail to reject Ho. We have convincing evidence of a useful linear relationship between growth rate and research and
development expenditure.
(b) Use a 90% confidence interval to estimate the average change in growth rate associated with a $1,000,000 increase in
expenditure. (Use technology to find the critical value. Round your answers to four decimal places.)
% per yr
Interpret the resulting interval.
O We are 90% confident that the mean change in research and development expenditure associated with a 1 percent
change in growth rate is in this interval.
O We are 90% confident that the mean change in research and development expenditure associated with a 1 percent
change in growth rate is outside this interval.
O We are 90% confident that the mean change in growth rate associated with a $1,000 increase in research and
development expenditure is in this interval.
O We are 90% confident that the mean change in growth rate associated with a $1,000 increase in research and
development expenditure is outside this interval.
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