Question

1. A sample of 36 observations is selected from a normal population. The sample mean is 21 , and the population standards deviation is 5 . Conduct a test of hypothesis using the 0.05 significance level. Null hypothesis =20 . Alternate = ?

2. A sample of 81 observations is taken from normal population with a standard deviation of 5 . The sample mean is 40 . Determine the 95 %confidence interval for the population.

3. Given the following sample observations which were randomly selected regarding the number of contacts in thousands of dollars represented by X, and the corresponding sales in thousands of dollars represented by Y,

Answer 1

1' level 5. A sample of M236 Observations is selected. The sample mean is, xz 21. the population Standard deviation (0)25... We have to test ab X 20.05 significan Неке бия, Null bypothesis, Ho: Mz 20. and Hail #20 Su, population mean (ro) = 20. As someone on standard deviation is given, we use as 7 test statistie here. The formula is given by 7, T-Mo 21-20 30.833 2120 Now, the evilinado ľvalue of this test is, .. pz 0.230 As p value > X 20.057 So, we cannot reject owe null hypothesis.

L A sample of 12 81 observation is taken. Now, Sample mean (1) 2 40 Vn Sample standard deviation (-1)2 5. As Sample Size (M) > 30 , bo, we use a Z test statistic bere. We have to construct a 95% confidence Interval for population mean (al). The formula is given by the equation - CI, £ ** & Cuitical value of z at 420005 is, - Za 10 645 . :- CT 40 + 1645 =(40-0.914, 4070.914) - 1391086, 401914) 3. The equation of regression Line is given by - ya bot bi x where bi: slope of line. boz y. inlercept Whiere, bia na X; Yi – ()CE.y). m2x^- x)^. and be • 8 - 97 ..

Нео, 1г 5 The data is given x y x2 ху 4 4 14 6 . gs 20 3. 5 ч 15 2 а 36 42 10 7 100 го 28 29 171 23. . . ь, 2, 5xt73 – 8 Х24 5 x 186 – (28) 2 .. 53 19. 2 р. 3. Во 2 x 29 – 0-36 ( x 30) , 5-8 - 2:04 2 3:18 Hence, the equation of elegression line, Yz bot bix. У 13:78 + 0.34 х. When X 212, the value of Yis, Уг 3 •79 +о - 36 х12. 2 8'' . . -

(@) when yz 10, the value of a is, 102 3.7870'36x. or, 0.36X 2 10-3078.26:22 . 6.22 . 0.36 or x 2 217.298 d) If We sterowa plot thee giren desa, then the scatten diagrań will look like 4. N waruno o' i 2 3 4 5 6 7 8 9 10 scatter diagram.