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Section C Regal Manufacturing CC was founded in 2009 and specialises in the manufacture of beauty soap, laundry soap, liquid hand soap, hospitality soap and

Section C

Regal Manufacturing CC was founded in 2009 and specialises in the manufacture of beauty soap, laundry soap, liquid hand soap, hospitality soap and detergents for sale to consumers of all income groups. The Marketing Director of the company wishes to know if customers have a preference for a bath soap fragrance. This information would help the Marketing Department in giving recommendations on the best flavour(s) to provide in the market. To answer their question, a random sample of 240 adult shoppers is offered a free bar of soap. The recipients may choose from among the four flavours. The choices are as follows:

Rose

Blue-lavender

Sandalwood

Lemon

66

53

45

36

Based on the above information, conduct a Chi-squared Goodness-of-Fit Test at 2% significance level. (15)

5.1 Formulated for the demands of professionals, Diamond Vogel Architectural Coatings offers a full range of architectural and heavy-duty protective coatings that are right for your project. Suppose that a paint supply general dealer wanted to estimate the correct amount of paint contained in five-litre cans purchased from Diamond Vogel Architectural Coatings. A random sample of 29 cans is selected, and the average amount of paint per five-litre can is 4.974 . It is known from the manufacturer's specifications that the sample standard deviation of the amount of paint is equal to 0.07 . Assume a normal distribution of fill.

5.1.1 Set up a 98% confidence interval estimate of the true population average amount of paint included in a five-litre can. (8)

5.1.2 Based on the results of (a), do you think that the general dealer has a right to complain to the manufacturer? Why? (3)

5.2 Production Logix, located in Pinetown, South Africa, is a leading Electronics Manufacturing Services (EMS) provider. A production manager at Production Logix wants to know whether the proportion of defective parts produced by machine A is no more than the proportion of defective parts produced by machine B. Formulate the null and alternative hypothesis appropriate for this management question. (4)

6.1 The South African Department of Health is concerned that the average percentage mark-up on a particular vitamin products during the dawn of covid-19 pandemic is 51% or more. To test their concern, they sampled 86 pharmacies that sell the product, and found that the mean percentage mark-up was 48.1%. Assume that the population standard deviation of the percentage mark- up is 14.7%.

6.1.1 What is the appropriate test statistic for this management scenario? Why? (3)

6.1.2 Formulate the null and alternative hypothesis for this test situation and conduct an appropriate statistical test at the 4% level of significance to determine whether the South African Department of Health's concern is justified. What conclusion can be drawn from the findings? (8)

6.2 When a claim or statement is made about the difference between two population means for the same random variable, the claim can be tested using the sampling distribution of the difference between two sample means. One example is: Is the average age of female shoppers at Truworths lower (i.e. are they younger?) than the average age of female shoppers at Foschini? Explain the kind of information that is required to perform such two-sample hypothesis tests. (4)

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