Question

5. Normally the leaves of the Mimosa pudica are horizontal. However, if one of them is touched lightly, the leaflets will fold. It is reported that y, the true mean time from touch to complete closure is 3.0s. An experiment is run to test this value. A random sample of size observations on the elapsed time (seconds) from touch to complete closure yields the following data: 3.2, 4.4, 3.5, 2.9, 4.2, 2.8. Assume the population distribution of elapsed times is normal. (a) Compute a 90% confidence interval for u. (b) Use the results of the sample as a pilot study to determine the sample size needed to estimate ji within 20.20s with 95% confidence. (c) Use the results of the sample as a pilot study to determine the sample size needed to estimate u within 20.30s with 95% confidence.

Answer 1

AutoSave OFF Xa Book1 Home Insert Draw Page Layout Formulas Data Review View XLSTAT & Tell me Connections f Y 0] > Clear Reapply Advanced El 2 EE Properties From HTML Stocks Geogra... Sort Filter From New Database Text Query Refresh All Z Edit Links Text to Flash-fill Remove Data Columns Duplicates Validatior H900 x ✓ fx F H - к L M N o P Q ا Descriptive Statistics 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 Mean Input OK X 3.2 4.4 3.5 2.9 4.2 2.8 Input Range: $G$900:$G$906 Cancel Grouped By: 3.5 0.27325202 3.35 #N/A 0.66932802 0.448 -1.80664063 0.4862286 1.6 2.8 4.4 21 Columns Rows Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Largest(1) Smallest(1) Confidence Level(90.0%) Labels in first row Output options 6 $H$900 4.4 2.8 0.55061604 Output Range: New Worksheet Ply: New Workbook 90% confidence interval = Mean Margin of error 3.5 +0.550616039 % 90 Summary statistics 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 (a) 90% confidence interval = 2.949383961 4.05061604 Confidence Level for Mean: Kth Largest: for 95 % confidence Margin of error = t0.05 for 5df * s/sqrt(n) 2.571*0.669328/sqrt (n) Kth Smallest: 1 now ME=0.20, so we have 0.20 = sqrt(n) = sqrt(n) = n= 2.571*0.669328/sqrt (n) 2.571*0.669328/0.20 8.604211713 74.0324592 933 (b) n= 74 934 935 936 937 938 when ME=0.30, so we have sqrt(n) = sqrt(n) = 2.571*0.669328/0.30 5.736141142 32.9033152 33 n= (C) n= 939 940 941 942 943 944 945 946 947

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