4. A small electronics store has begun to advertise in the local newspaper. Befo

Question

4. A small electronics store has begun to advertise in the local newspaper. Before advertising, the long term mean weekly sales were $9820. A random sample of 10 weeks while the newspaper ads were running had a sample mean of $10,960 and a sample standard deviation of $1580. From previous data, the distribution of weekly sales is known to be approximately a normal distribution. At the 5% significance, does the data provide sufficient evidence to claim that the population mean weekly sales is now more than $9820. (a) State the null and alternate hypotheses. (b) What is the level of significance? (c) Is this a right-tailed, left-tailed, or two-tailed test? (d) List each assumption and show information to determine if the assumptions are met for testing this hypothesis. (e) Which of the following test procedures is used to test the hypothesis stated in part (a)? NOTE: COMPUTATION OF THE P-VALUE NOT REQUIRED a. One mean - Z test b. One Mean-t test c. Cannot do test (State why) (1) If the p-value is 0.0242, is Ho rejected or not? (9) Write the interpretation of the results of the hypothesis test. nglish

Explanation / Answer

Question 4.

(a) Null Hypothesis : H0 : Population mean sales is equal to $9820. = $ 9820

Alternative Hypothesis : Ha : Population mean sales is more than $ 9820.   > $ 9820

Here sample mean x = $ 10960

Sample standard deviation s = $ 1580

Standard error of the sample mean = s/ sqrt(n)= 1580/ sqrt(10) = $ 499.64

(b) Level of significance = 0.05

(c) The test is a right - tailed test.

(d) Assuption of one sample hypothesis testing are

(i) Samples are randomly drawn.

(ii) Minimum variance of sample size.

(iii) No outliers or biasedness

(e) We will use one mean t - test.

t = (10960 - 9820)/ 499.60 = 2.28

(f ) p - value = 0.0242 so it is less than 0.05 so we shall reject the null hypothesis .

(g) We can interpret that the mean weekly sales is now more than $ 9820

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