# A researcher wishes to test the claim that the mean cost of tuition fees at a four-year private college for one semester is greater: Business Statistics Assignment, UU, Malaysia

University | Ulster University (UU) |

Subject | Business statistics |

**Question 1**

**a)** A researcher wishes to test the claim that the mean cost of tuition fees at a four-year private college for one semester is greater than RM 6,900. He selects a random sample of 40 four-year private colleges and finds the mean to be RM 7,200. The population standard deviation is RM 724. Use a=0.05 to determine whether the mean cost of tuition fees at a four-year private college for one semester is greater than RM 7,200.

- Identify the claim and state the HO and H1.
- Find the critical value.
- Calculate the test statistic.
- Make a decision to reject or fail to reject the HO.
- Interpret the decision in the context of the original claim.

**b)** According to payscale.com, the mean starting salary for a Lawyer is RM 79,500 a year. A researcher wishes to test the claim that the starting salary is less than RM 79,500 a year. A random sample of 8 Lawyers is selected and the sample means salary is RM 79,150 a year. Assume that the data belong to a normal population and the sample standard deviation is RM 6,937.68. Test the claim at a=0.10.

- Identify the claim and state the HO and H1.
- Find the critical value.
- Calculate the test statistic.
- Make a decision to reject or fail to reject the HO.
- Interpret the decision in the context of the original claim.

**c)** It has been found that 50.3% of Malaysian Households own ASB accounts. A random sample of 300 heads of households indicated that 171 owned ASB accounts. Use a=0.05 to test the claim that there is a difference in the proportion of Malaysian households who own ASB accounts.

- Identify the claim and state the HO and H1.
- Find the critical value.
- Calculate the test statistic.
- Calculate the p-value for the test
- Make a decision to reject or fail to reject the 1-10.

**Question 2**

**a)** The table below shows the number of 25 defective rice cookers on a particular production day.

- Construct a frequency distribution.
- Using the result from Part, calculate the relative frequencies for each class.
- Using the result from Part, calculate the cumulative frequencies for each class.
- Construct a frequency histogram for these data.
- Using the result from Part, compute the mean.
- Using the result from part, compute the standard deviation.

**b)** The following stem and leaf display shows the expenditure on clothes for work by professional men. The data is in RM.

- How many professional men were involved in this study?
- How many professional men are there in the third class?
- How many professional men spend more than RM 7,000 on clothes?

**Question 3**

A manufacturer carried out a survey of the defects in their toys. It is found that the probability of a toy having poor stitching is 0.03 and that toy with poor stitching has a probability of 0.7 of splitting open. A toy without poor stitching has a probability of 0.02 splitting open. Based on the information given:

- Draw a tree diagram and find the expected value for each situation.
- If the soft toy randomly chooses, find the probability a soft toy with poor stitching and splitting open is chosen.
- The manufacturer also finds that soft toys can become faded with a probability of 0.05 and that this defect is independent of poor stitching or splitting open. A soft toy is chosen at random. Find the probability the soft toy has exactly one of these 3 defects.

Question 4

The table below is the age distribution of employees in SMP Sdn Bhd.

Based on the sample data given, compute the variance and standard deviation.

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