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1. The share of the national car manufcturers market in South Africa is shown in the table below:
MANUFACTURER % OF SHARES
VW 37
Toyota 30
Delta 15
BMW 10
Mercedes 8
A random sample of 2000 car owners in Pretoria revealed the following ownership pattern:
VW = 758 Toyota = 680 Delta = 300 BMW = 162 Mercedes = 100
Does the ownership pattern differ significantly from the National pattern?Investigate at the 5% level of significance.
2. It is believed that call centre operators should spend no longer than 10 minutes on each call, however a survey involoving a random sample of 49 operators found a mean call duration of 11 minutes with a standard deviation of 3 minutes. Test the Hypothesis at the 1% level of significance.
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Continuous random variable is uniformly distributed between a and b. The probability density function between a and b is.
The mean math score for fifth grade students at Smart Elementary is 90 with a standard deviation of 8. The fifth grade students are tested each year to determine if the mean score remains the same.
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In a sample of 88 children selected randomly from one town, it is found that 8 of them suffer from asthma. Find the P value for a test of the claim that the proportion of all children in the town who suffer from asthma is equal to 11%.
A number of years ago, there was a popular television game show called Let's Make a Deal. The host Monty Hall, would randomly select contestants from the audience and, as the title suggests
The height in inches of girls on a high school girls basketball team are as follows: Identify the z score used in a quantile plot for the player with a height of 66.5 inches.
Supposing that both populations are normally distributed, construct a 99% confidence interval for the ratio of the two population variances.
Find out the range (R), variance (V) and standard deviation (s) for the given set of values:
Show that theta~ = u(X) is an unbiased estimator of theta, where u(0) = 1 and u(x) = 0 if x =1,2, ... Compare the MSEs of theta(hat) and theta~ for estimating theta = e^(-m) when m=1 and m=2
Suppose a botanist grows many individually potted eggplants, all treated identically and arranged in groups of four pots on the greenhouse bench.
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