Conduct a hypothesis test to evaluate if these data provide evidence of a difference between the proportions of truck drivers and non-transportation workers (the control group) who get less than 6 hours of sleep per day, i.e. are considered sleep deprived. The test statistic is: Z = The P-value is **Table: Sleep Duration Among Transportation Professionals**This table presents the distribution of sleep duration among different groups, including a control group and various categories of transportation professionals: pilots, truck drivers, train operators, and bus/taxi/limo drivers.| Sleep Duration | Control | Pilots | Truck Drivers | Train Operators | Bus/Taxi/Limo Drivers ||-------------------------------|---------|--------|---------------|-----------------|-----------------------|| **Less than 6 hours of sleep** | 35 | 19 | 35 | 29 | 21 || **6 to 8 hours of sleep** | 193 | 132 | 117 | 119 | 131 || **More than 8 hours** | 64 | 51 | 51 | 32 | 58 || **Total** | 292 | 202 | 203 | 180 | 210 |- **Control Group**: Represents a baseline group for comparison, as seen with the highest reporting of 6 to 8 hours of sleep (193 individuals).- **Transportation Professionals**: - **Pilots**: Majority (132) get 6 to 8 hours of sleep, with fewer sleeping less than 6 hours (19) or more than 8 hours (51). - **Truck Drivers**: An equal number of individuals report less than 6 hours and more than 8 hours of sleep (51 each), but most get 6 to 8 hours (117). - **Train Operators**: Similar to truck drivers, with a majority sleeping 6 to 8 hours (119). - **Bus/Taxi/Limo Drivers**: Show a distribution with the majority getting 6 to 8 hours of sleep (131), and the least number getting less than 6 hours (21).This data provides insight into sleep patterns across different transportation sectors, highlighting variations in sleep duration preferences and potential areas for sleep-related interventions.

State the hypotheses. Obtain the value of the test statistic. The value of test statistic is obtained below: The value of sample proportion1, Thus, the value of test statistic is 1.649Obtain the P-value. Use Excel to obtain the probability value for Z=1.649 Follow the instruction to obtain the P-value: Open EXCEL Go to Formula bar. In formula bar enter the function as“=NORMSDIST” Enter the test statistic Z as 1.649 Click enter EXCEL output: From the Excel output, the P-value is 0.9504 The P-value in right tail is 0.0496 The P-value in two tail is 0.0992(=2*0.0496). Thus, the P-value is 0.0992 The conclusion is obtained as shown below: Use the level of significance is 0.05. The p-value is greater than level of significance. By rejection rule, do not reject the null hypothesis. That is, there is no difference between the proportions of truck drivers and non-transportation workers (the control group) who get less than 6 hours of sleep per day.

Math

Statistics

Conduct a hypothesis test to evaluate if these data provide evidence of a difference between the proportions of truck drivers and non-transportation workers (the control group) who get less than 6 hours of sleep per day, i.e. are considered sleep deprived. The test statistic is: Z = The P-value is

Conduct a hypothesis test to evaluate if these data provide evidence of a difference between the proportions of truck drivers and non-transportation workers (the control group) who get less than 6 hours of sleep per day, i.e. are considered sleep deprived. The test statistic is: Z = The P-value is

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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