If interest rates are at a level of 1% and expected inflation is 2%, would you prefer saving or spending your money?

1 answer:

6 0

If interest rates are at a level of 1% and expected inflation is 2%, it would be preferable to spend your money instead of saving it.

Suppose you have $100 and you save it in a savings account that pays a 1% interest rate. After a year, you will have $101 in your account.

During this period, if inflation runs 2%, you would have to have $102 to make up for the impact of higher prices.

Since you will only have $101 in your account, you have actually lost some purchasing power.

If your savings don’t grow to reflect this rise in prices over time, the effect will be as though you are actually losing money.

This means that if you have $100 which you can use to buy a TV set, and you saved the money instead is a savings account that pays 1% interest.
After 1 year, because of inflation of 2%, the TV set now costs $102 whereas the money in your bang account wil be $101.

Thus, you actually need to get an extra $1 from somewhere to fund the TV set you could have been able to buy a year ago.

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A 2003 study of dreaming found that out of a random sample of 106 people, 80 reported dreaming in color. However, the rate of

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Step-by-step explanation:

Hello!

You have the following experiment, a random sample of 106 people was made and they were asked if they dreamed in color. 80 persons of the sample reported dreaming in color.

The historical data from the 1940s informs that the population proportion of people that dreams in color is 0.21(usually when historical data is given unless said otherwise, is considered population information)

Your study variable is a discrete variable, you can define as:

X: Amount of people that reported dreaming in colors in a sample of 106.

Binomial criteria:

1. The number of observation of the trial is fixed (In this case n = 106)

2. Each observation in the trial is independent, this means that none of the trials will have an effect on the probability of the next trial (In this case, the fact that one person dreams in color doesn't affect or modify the probability of the next one dreaming in color)

3. The probability of success in the same from one trial to another (Or success is dreaming in color and the probability is 0.21)

So X~Bi(n;ρ)

In order to be able to run a proportion Z-test you have to apply the Central Limit Theorem to approximate the distribution of the sample proportion to normal:

^ρ ≈ N(ρ; (ρ(1-ρ))/n)

With this approximation, you can use the Z-test to run the hypothesis.

Now what the investigators want to know is if the proportion of people that dreams in color has change since the 1940s, so the hypothesis is:

H₀: ρ = 0.21

H₁: ρ ≠ 0.21

α: 0.10

The test is two-tailed,

Left critical value: $Z_{\alpha/2} = Z_{0.95} = -1.64$

Right critical value: $Z_{1-\alpha /2} = Z_{0.95} = 1.64$

If the calculated Z-value ≤ -1.64 or ≥ 1.64, the decision is to reject the null hypothesis.

If -1.64 < Z-value < 1.64, then you do not reject the null hypothesis.

The sample proportion is ^ρ= x/n = 80/106 = 0.75

Z= 0.75 - 0.21 = 12.83

√[(0.75*0.25)/106]

⇒Decision: Reject the null hypothesis.

p-value < 0.00001 is less than 0.10

If you were to conduct a one-tailed upper test (H₀: ρ = 0.21 vs H₁: ρ > 0.21) with the information of this sample, at the same level 10%, the critical value would be $Z_{0.90}$ 1.28 against the 12.83 from the Z-value, the decision would be to reject the null hypothesis (meaning that the proportion of people that dreams in colors has increased.)