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SMO makes hardware components in its factory in the UK and currently uses two machines to fill the components. A sample of 30 components from the first machine has a mean weight of 190 g and a standard deviation of 40 g. A sample of 40 packets from the second machine has a mean weight of 180 g and a standard deviation of 10 g. State the six-point procedure for hypothesis testing and test if the two machines are comparable in terms of putting the same amount in packets
The idea of buying a new PC machine to replace the older one arose at the last management team meeting. The older one would not be sold but could be used as backup if necessary. If SMO does decide to replace the older machines and buy new ones, the finance dept has indicated that the maximum monthly payment they could afford, based on current profit forecasts for the next six years, would be £2000 p.m. The Company’s bankers would be able to offer an interest rate of 4% to borrow the £95,000 cost of the new machine. What range of months would you recommend that the loan is taken over to keep within SMO’s budget?
Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 12 of the 57 boxes on the shelf have the secret decoder ring. The other 45 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring?
In a large population, 58% of the people have been vaccinated. If 5 people are randomly selected, what is the probability that at least one of them has been vaccinated?
During the pandemic, online ordering of groceries and household supplies was offered by many stores as an accommodation for shoppers who preferred not to visit crowded stores in person. An online grocery shopping service claims that its mean delivery time is less than 120 minutes with a population standard deviation of 30 minutes. A random sample of 49 orders is delivered with a mean of 100 minutes. At the 95% confidence level, is there enough evidence to support the claim? Assume the data are normally distributed. Use the critical value method and respond to the prompts below.
A random sample of 30 households was selected as part of a study on electricity usage, and the number of kilowatt-hours (kWh) was recorded for each household in the sample for the March quarter of 2020. The average usage was found to be 375kWh. In a very large study in the March quarter of the previous year it was found that the standard deviation of the usage was 85kWh. Assuming the standard deviation is unchanged and that the usage is normally distributed provide an expression for calculating a 99% confidence interval for the
mean usage in the March quarter of 2020
A fair coin tossed 400 times.If X is the number of heads obtained, find the expected value and variance of X
A random sample of 25 first year students is drawn. The table below shows the result of an analysis carried out.
Test of Mu = 76 vs Mu < 76
Variable Mean Std Dev SE Mean P-Value
Score 77.25 13.13 * **
a) Explain what the statistician is doing here?
b) Classify this test according to Left, Right or two Tailed.
c) Calculate the missing value * and use the tables provided to approximate the value of **.
d) If you were the statistician, what would you conclude and why?
Suppose that in the past, 54% of all adults favored capital punishment. Do we have a reason to believe that the proportion of adults favoring capital punishment today has increased if, in a random sample of 43 adults, 32 favor capital punishment? Use a 0.1level of significance.
At a certain college, it is estimated that fewer than 75% of the students have cars on campus, and with this number, the parking lot is fully occupied. Would you suggest to increase the parking lot space if, in a random sample of 60 college students, 55 are found to have cars? Use 0.1 level of significance.
