How much customers buy is a direct result of how much time they spend in the store. A study of average shopping times in a large national houseware store gave the following information (Source: Why We Buy: The Science of Shopping by P. Underhill). Women with female companion: 8.3 min. Women with male companion: 4.5 min. Suppose you want to set up a statistical test to challenge the claim that a woman with a female friend spends an average of 8.3 minutes shopping in such a store. (a) What would you use for the null and alternate hypotheses if you believe the average shopping time is less than 8.3 minutes?

Null Hypothesis [H0] : t = 8.3

Alternate Hypothesis [H1] : t < 8.3

Step-by-step explanation:

Hypothesis testing is used to test the statistical significance of a mathematical proposition.

Null Hypothesis is the neutral hypothesis, stating equality to assumed value. Alternate Hypothesis is the contradictory hypothesis, stating deviation from the assumed value.

For hypothesis formation of given case:-

Let average time taken by women with female companion = t

Null Hypothesis [H0] : t = 8.3

Alternate Hypothesis [H1] : t < 8.3

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.