As the principal, interest rate, and compound periods increase, so does the future value of an investment. It doesn't matter if you are just putting some money into short-term, low rate savings accounts or CDs or long-term, higher return investments, compound interest will work for your benefit if you allow it.

Step-by-step explanation:

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Chloe breaks into the pantry after Albert goes to work. She finds and opens a family-pack of mixed nuts. After surfing the web,

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Solution :

In this case we have to use $\text{chi square test}$ for the goodness of fit.

Null hypothesis is : $H_0 :$ Data follows the given distribution

Alternate hypothesis is : $H_a:$ Data do not follow the given distribution

The level of significance, $\alpha = 0.05$

The test statistics is given by :

Chi square = $\sum\frac{(O-E)^2}{E}$

Here O is the observed frequencies

E is the expected frequencies

So we have, N = number of the categories = 4

df = degrees o freedom = N - 1

= 4 - 1 = 3

Critical value = $7.814727764$

Calculating the table for the test statistics are given as :

Category prop. O E $\frac{(O-E)^2}{E}$

A 0.2 14 20 1.80

C 0.3 28 30 0.13

M 0.1 6 10 1.60

P 0.4 52 40 3.60

Total 1 100 100 7.13

The test statics = chi square = $\sum\frac{(O-E)^2}{E}$ = 7.13

$X^2$ statistics = 7.13

P-value = 0.067767248

P -value > $\alpha = 0.05$

Therefore, we do not reject the $\text{null hypothesis}$ . There is sufficient evidence to conclude that the data follows the given distribution. So there is sufficient evidence to conclude the given claim is true.