The answer choices below represent different hypothesis tests. which of the choices are left-tailed tests? select all correct answers. select all that apply:
a) h0: x=17.3, ha: x≠17.3
b) h0: x=19.7, ha: x< 19.7
c) h0: x=11.2, ha: x< 11.2
d) h0: x=13.2, ha: x≠13.2
e) h0: x=17.8, ha: x> 17.8

Step-by-step explanation:

We know that the type of hypothesis test depends upon the nature of alternative hypothesis . If the alternative hypothesis is left-tailed then the test is also left-tailed.

Similarly for right tailed and two tailed hypothesis.

From the given options , the set of hypothesis with left-tailed alternative hypothesis are :-

Therefore , in choices B) and C) , the hypothesis test is left-tailed test.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}