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In: Math

(Please type out. I struggle to read handwriting.) 2. Collette is self-employed and sells cookware at...

(Please type out. I struggle to read handwriting.)

2. Collette is self-employed and sells cookware at home parties. She wants to estimate the average amount a client spends at each party. A random sample of 35 receipts gave a mean of x̅ = $34.70 with standard deviation s = $4.85.

(a) Find a 90% confidence interval for the average amount spent by all clients.

(b) What conditions are necessary for your calculations?

(c) For a party with 35 clients, use part (a) to estimate a range of dollar values for Collette’s total sales at that party.

Solutions

Expert Solution

we want to construct the 90% confidence interval for the average amount spent by all clients

Given that

Sample mean

Sample SD = s = 4.85

Sample size = n = 35

Confidence level = C = 0.90

90% confidence interval for the average amount spent by all clients

Where ,

DF = n - 1 = 34

tc = 1.691    ..............( From t table )

90% confidence interval for the average amount spent by all clients

.......................( ANSWER)

=====================================================================================

B) conditions are necessary for your calculations are as follows

1) The parent distribution of data should be normal.

2) The sample should be random.

3) The population Standard deviation is unknown

====================================================================================

C) we want to estimate a range of dollar values for Collette’s total sales at that party when n = 35

Therefor Lower limit = 35 * 33.314 = 1165.99    

Upper limit = 35 * 36.086 = 1263.01

The range of dollar values for Collette’s total sales at that party is (1165.99 , 1263.01)


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