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Two coins are tossed. Let T be the number of tails that occurs. Determine the values
of the random variable T.
A company estimates that 0.2% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $500.
If they offer a 2 year extended warranty for $31, what is the company's expected value of each warranty sold?
.There are four cars available for comparative study of tyre performance .It is believed that tyres are wearing out in a different rate at different positions of a car. Tyres were installed in four different locations: Right - Front, Left - front, Right - rear and left - rear. The measurements of the wearing out of tyres in this investigation are noted. Three factors are considered in this study . They are tyre position, car and the different tyres studied in this investigation.
Annova Table
Source Sum of squares df mean square F Sig.
car 2036 3 679 28.77 0.001
position 359 3 120 5.07 0.044
Tyre types 381 3 127 5.38 0.039
Error 142 6 24
total 47,016 16
a. identify the type of design
b. identify the extraneous variables
c. find out the number of observation
d. formulate the hypothesis
e. interpret the result at 5% level of significance
A manufacturer of electric bulbs claims that his bulbs have a mean life of 25 months with a standard deviation of 5 months. A random sample of 6 such bulbs were taken and their lifespan were recorded.
Life of bulbs(in months):23 25 30 20 20 12
Is the manufacturer's claim valid at 1% level of significance when the table value of t test is ±4.032?
(a) Formulate a null and alternative hypothesis.
(b) Calculate the mean, standard deviation, and the tSTAT.
(c) Interpret the manufacturer's claim.
I answered a and b but c made me confused. can anyone help me?
the choices ;
A.
The null hypothesis is rejected as tSTAT is less than the table value. Hence the manufacturer's claim is not valid at 1% level of significance.
B.
The null hypothesis is not rejected as tSTAT is more than the table value. Hence the manufacturer's claim is valid at 1% level of significance.
C.
The null hypothesis is not rejected as tSTAT is less than the table value. Hence the manufacturer's claim is valid at 1% level of significance.
D.
The null hypothesis is rejected as tSTAT is more than the table value. Hence the manufacturer's claim is not valid at 1% level of significance.
A popular confectionary brand manufacturing "dips and salad dressings" wants to understand what should be the value proposition that it should use to position itself in the minds of consumers. The company asked the respondents to rate Thousand Island dressing on the following parameters and run factor analysis to come up with a solution:
V1 Authentic
V2 Nutritious
V3 Healthy
V4 Good Ingredients
V5 Tangy
V6 Sweet and Sour
V7 Tasty
V8 Expensive
V9 Economical
The output factor analysis is presented below:
KMO and Bartlett's Test
Kaiser - Meyer - Olkin Measure of sampling .888
Adequacy
Bartlett"s Test of Approx. chi - square 800. 400
Sphericity Df 36
sig .000
Total Variance Explained
Intial Eigenvalues Extraction sums of squared loadings
component Total % of variance cumlulative % Total % of variance cumulative%
1 3.066 30.067 30.067 3.066 30.067 30.067
2 2.021 26.451 56.517 2.021 26.451 56.517
3 1.209 16.436 72.953 1.209 16.436 72.953
4 .679 7.548 77.501
5 .585 6.498 83.999
6 .493 5.481 89.480
7 416 4.623 94.103
8 .303 3.368 97.471 .
9 .228 2.529 100.000
Rotated Component Matrix
Component
1 2 3
V3 865 -230 .020
V4 778 200 .080
V6 .080 .804 .170
V8 .040 .054 -8.53
V9 .119 .209 .762
V2 880 -.128 -.001
V1 .858 -.118 .026
V5 -.120 .771 -.076
V7 -.160 .775 .095
Extraction Method: Prinicipal Component Analysis.
Rotation Method: Varimax with Kaiser
Normalization.
Rotation converged in 4 iterations.
Based on the above output tables, answer the following questions:
a. does the factor analysis give significant results? interpret KMO and Bartlett's.
b. Based on eigen values how many factors are emerging?
c. what percentage of variation is explained by those factors?
d. what are the variables better represented by each factor?
e. identify the surrogate variable for each other
f. give a suitable name to the factors
The mean weekly sales of soap bars in departmental stores was 146.3 bars per store.
After advertising campaign the mean weekly sales in 22 stores for a typical week
increased to 153.7 and showed a standard deviation of 17.2. Was the advertising
Campaign successful?
An unbiased die is thrown find out the probability of getting
Prime number
Odd number
Even number
A multiple of 2&3
Number less than 7
A multiple of 4 ?
(a) Let X be a random variable with the following probability distribution x -3 6 9 f(x) 1 6 1 2 1 3 Find the mean and variance of Y = 3X + 2. (b) If X ∼ Bin(6, 1 3 ) and Y ∼ N( 1 2 , 1 4 ) are independent random variables, find the mean and variance of the random variable W = 2X − 4Y + 5.
A card is drawn from a standard deck of 52 cards and then a second card is drawn without replacing the first card. If we know that the second card is a spade, what is the probability that the first card is a spade?
A certain high quality commercial light bulb has an estimated lifetime of µ = 750 hours with a variance σ 2 = 100. If 20,000 bulbs are installed in city street lights. (a) Use Chebyshev’s inequality to estimate how many of these bulbs will live between 735 and 765 hours. (b) Use the normal distribution to determine how many of these bulbs will live between 735 and 765 hours. (c) Does your answer in (b) verify Chebyshev’s inequality results?
