# 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

School

###### Ulster University (UU)

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Assignment Type

Subject

Date

###### 19/12/2022

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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