Question

State the hypotheses and identify the claim, find the critical value(s), compute the test value, make the decision, summarize the results (make the appropriate statement of the results of the claim included rejection or non-rejection of the null hypothesis). Please show all of your work.

3)The number of annual precipitation days for one-half of the 50 largest U.S. cities is listed below. Do the following: 131 94 136 88 116 77 127 79 47 97 116 123 88 102 27 80 156 133 117 55 112 98 55 90 125

a)Construct a frequency distribution for the data (include class boundaries in the table) with 5 classes.

b)Graph its histogram. c)Plot its cumulative frequency (ogive).

d)Find the mode of the data.

e)Find the mean, for the grouped data.

f)Find the variance and standard deviation for grouped data.

g)Find the z score and percentile for the value 98.

Answer 1

a)Construct a frequency distribution for the data (include class boundaries in the table) with 5 classes.

A B c D K L M N 0 P Q R S T Frequency Histogram Class Cou interal Frequency Class Width Midpoint 10 9 8 7 F H J Cumulative Relative Cumulative Class Boundaries RelativeFrequ frequency frequency ency 4026.5-53.5 0.08 2 0.08 66 52.5-79.5 0.12 5 0.20 92 78.5-105.5 0.36 14 0.56 118 104.5–131.5 0.28 21 0.84 144130.5–157.5 0.16 25 1.00 127-53 25379 3 79105 4 105_131 5131157 2 3 9 3 4 5. 6 26 26 26 26 26 5 7 Frequency of Occurance 4 6 3 2 7 Total 25 0.04 8 9 10 11 2753 5379 7 105 105 131 131" 157 class interval

Formula Reference:

b)Graph its histogram:

Frequency of Occurance ONWA Choco 27-53 53~- 79 Frequency Histogram 79 105 Class interval 105-131 131 157

c)Plot its cumulative frequency (ogive):

A B o D E L M N 0 Р R S T vo Class interal Cou + Frequency Class Width Midpoint Ogive 30 2 3 127253 2 5379 3179-105 4105131 5131157 F G H Cumulative Relative Cumulative Class Boundaries Relative Frequ frequency frequency ency 4026.5-53.5 0.08 2 0.08 66 52.5-79.5 0.12 5 0.20 92 78.5–105.5 0.36 14. 0.56 118 104.5–131.5 0.28 21 0.84 1441130.5–157.5 0.16 25 1.00 3 4 5 6 9 26 26 26 26 26 Frequency 7 4 7 Total 25 1 0.04 40 66 92 118 144 8 9 10 11 Midpoint

Ogive:

Ogive Frequency 0 40 66 92 118 144 Midpoint

d)Find the mode of the data:

Calculate Mode, Percentiles-98 from the following grouped data Class Frequency 27-53 53 - 79 79 - 105 105 - 1317 131 - 1574 تهاني | ه ا ہد | كل Frequency of Solution: Class (1) 27-53 53 - 79 79 - 105 105 - 131 131 - 157 2 3 9 2 5 14 21 25 7 4 n = 25 To find Mode Class Here, maximum frequency is 9. · The mode class is 79 - 105. · 1 = lower boundary point of mode class = 79 :-fi = frequency of the mode class = 9 - fo = frequency of the preceding class = 3 .: = frequency of the succedding class = 7 ..c= class length of mode class = 26 Z= L = f1-to | 2 - f - 10 - 12 9-3 = 79 - 3.-) 26 12.9-3. 6 = 79+ (6) 26 = 79 +19.5 = 98.5

Mean,variance and std dev:

D fx B с Midpoint Frequency 40 66 92 118 144 2 3 E F (x-u)^2 f*(x-u)^2 80 3638.50 7277.00 198 1177.86 3533.59 828 69.22 623.00 826 312.58 2188.08 576 1907.94 7631.77 7 4 А 1 Values 2 27-53 3 5379 4 79105 5 105-131 6 131157 7 8 9 10 11 12 13 14 15 Mean 25 2508' 7106.11 21253.44 460 100.32 16 Variance Std Dev 850.14 29.16 17 18 19

Formula Reference:

А D F B Midpoint Frequency =(RIGHT(A2,2)+LEFT(A2,2))/2 2 =(RIGHT(A3,2)+LEFT(A3,2))/2 3 =(RIGHT(A4,3)+LEFT(A4,2))/2 9 =(RIGHT(A5,3)+LEFT(A5,3)}/ 27 = (RIGHT(A6,3)+LEFT(A6,3))/2 4 fx =B2*C2 =B3*C3 =B4*C4 =B5*C5 =B6*C6 E (x-u)^2 =(B2-$B$15)^2 =(B3-$B$15)^2 =(B4-$B$15)^2 =(B5-$B$15)^2 =(B6-$B$15)^2 f*(x-u) 2 =C2E2 =C3*E3 =C4E4 =C5*E5 =C6*E6 1 Values 2 2753 3 5379 4 79105 5 105-131 6 131157 7 8 9 10 11 12 13 14 15 Mean 16 17 18 19 20 =SUM(C2:09) =SUM(D2:09) =SUM(B2:B11) =D14/C14 =SUM(E2:E11) =SUM(F2:F9) Variance Std Dev =F14/C14 =SQRT(E16)

Percentile:

Here, n = 25 P98 class : 987th Class with 100 value of the observation in of column 98 - 25 value of the observation in of column 100 = (24.5)' value of the observation in of column and it lies in the class 131 - 157. :: Pgg class : 131 - 157 The lower boundary point of 131 - 157 is 131. .: L = 131 981 100-cf Pos = L- = 131+ 24.5 - 21 - 26 4 = 131+ 3.5 4 - 26 = 131 + 22.75 = 153.75

z score:

z = (x - μ) / σ

z = (98 - 100.32) / 29.16

z = -0.08