Question

a) What is an hypothesis? [2 Marks]
b) Suppose that shopping times for customers at Cheers Hypermarket are normally
distributed with a known population standard deviation of 20 minutes. Suppose
that a random sample of 64 shoppers had a mean time of 75 minutes. Construct a
95% confidence interval for the population mean time. [6 Marks]
c) Petronellah, a Human Resource Manager at a large corporation, wanted to
estimate a proportion of the corporation’s employees who favor a modified bonus
plan. From a random sample of 344 employees, it was found that 261 were in favor
of this particular plan. Find a 90% confidence interval estimate of the true
population proportion that favors this modified bonus plan. [6 Marks]
d) A politician claims that more than 50% of females vote in presidential elections. A
random sample of 500 female registered voters from a particular ward showed that
275 of them voted in the last presidential election. Test the politician’s claim at 5%

level of significance.

[6 Marks] [TOTAL: 20 MARKS

Answer 1

(a)

Hypothesis: A Statement about the Population is known as Hypothesis.

Statistical Hypothesis: A Statement in terms of population parameter ( or Parameters ) is known as a Statistical Hypothesis and is denoted by H. In entire testing of hypothesis, a hypothesis means it is a Statistical Hypothesis.

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(b) Given Population Standard Deviation =

Given Sample size = n = 64 ( Large Sample )

Sample Mean =

Since Confidence Inteval = 95%

Therefore

Since Sample Size i.e n = 64 which is large number

So Citical Value will be as follows

Marginal Error:

Therefore 95% Confidence Interval of Population of   is

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(c) We know that x

Given Sample Size = n = 344 ( Large Sample )

Given x = 261

We know that

Standard Error of p:

Since Confidence Interval = 90%

So

Marginal Error:

Therefore the 90% Confidence Interval of "P" is

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(d) We frame the Hypothesis

Since : So, it's a One Tailed (Right Tailed ) Hypothesis Test.

So We can use Modulous in numerator of the Formula.

To test the we use the Z - Statistic

Where

We know that

Given Sample Size = n = 500 ( Large Sample )

x = 275

We know that

Given P= 50% = 0.5

Since Levell of Significant is

So, We Reject at 5% Leval of Significant.

Therefore we conclude that

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NOTE: To See the Critical Values of Z; we use the Standard Normal area tabulated values which i posted below.

How to see?

If alpha = 5% the confidence interval = 95%

Divide the value 95 with 100. you will get 0.95 and after that divide the value 0.95 with 2; you will get 0.475. Now Search this 0.475 in side the table ( repeating again see inside the table). You will find this at the intersection of (1.9, 0,06) which is Zcri value i.e 1.96.

Like this you can find the Zcri for any alpha values.